Delay and Its Time-Derivative Dependent Stable Criterion for Differential-Algebraic Systems
|
|
- Joshua Chambers
- 6 years ago
- Views:
Transcription
1 Applied Maemaics Publised Online June 6 in SciRes p://wwwscirporg/journal/am p://dxdoiorg/46/am67 Delay and Is ime-derivaive Dependen Sable Crierion for Differenial-Algebraic Sysems Hui Liu Yucai Ding Scool of Science Souwes Universiy of Science and ecnology Mianyang Cina Received April 6; acceped June 6; publised 4 June 6 Copyrig 6 by auors and Scienific Researc Publising Inc is work is licensed under e Creaive Commons Aribuion Inernaional License (CC BY) p://creaivecommonsorg/licenses/by/4/ Absrac In is paper e sable problem for differenial-algebraic sysems is invesigaed by a convex opimizaion approac Based on e Lyapunov funcional meod and e delay pariioning approac some delay and is ime-derivaive dependen sable crieria are obained and formulaed in e form of simple linear marix inequaliies (LMIs) e obained crieria are dependen on e sizes of delay and is ime-derivaive and are less conservaive an ose produced by previous approaces Keywords Differenial-Algebraic Sysems Sabiliy Analysis Lyapunov-Krasovskii Funcional Delay Pariioning Approac Linear Marix Inequaliy (LMI) Inroducion Differenial-algebraic sysems also referred o as singular sysems descripor sysems or generalized sae-space sysems arise in a variey of pracical sysems suc as cemical processes nuclear reacors biological sysems elecrical neworks and economy sysems Differenial-algebraic sysems include no only dynamic equaions bu also saic equaions [] []; e sudy of suc sysems is muc more complicaed an a for sandard saespace sysems e exisence and uniqueness of a soluion o a given differenial-algebraic sysem are no always guaraneed and e sysem can also ave undesired impulsive beavior wic can lead o e insabiliy and poor performance [] Because of e exensive applicaions in many pracical sysems a grea number of fundamenal noions and resuls in conrol and sysem eory based on sandard sae-space sysems ave been exended successfully o How o cie is paper: Liu H and Ding YC (6) Delay and Is ime-derivaive Dependen Sable Crierion for Differenial-Algebraic Sysems Applied Maemaics 7 4- p://dxdoiorg/46/am67
2 H Liu Y C Ding differenial-algebraic sysems In recen years muc aenion as been focused on sabiliy robus sabiliy and H conrol problems for differenial-algebraic sysems and some resuls ave been derived using e ime domain meod [4]-[] e exising resuls can be classified ino wo ypes: delay-dependen condiions wic include informaion on e size of delays [] [] and delay-independen condiions wic are applicable o delays of arbirary size [4] [5] Since e sabiliy of sysems depends explicily on e ime-delay e delay-independen condiions are more conservaive especially for small delays Wile e delay-dependen condiions are usually less conservaive and e conservaism will dependen on e cosen of Lyapunov funcional e inequaliy bounding ecnique and so on wo approaces were used o prove e sabiliy of e sysem in e exising lieraure e firs approac consiss of decomposing e sysem ino fas and slow subsysems and e sabiliy of e slow subsysem is proved using some Lyapunov funcional en e fas variables are expressed explicily by an ieraive equaion in erms of e slow variables [6] e second approac consiss of consrucing a Lyapunov-Krasovskii funcional a corresponds direcly o e descripor form of e sysem [7] Some oer meods ave also been provided o reduce e conservaive for example convex analysis meod [8] and delay pariioning approac [9] [] o e bes of our knowledge mos of e exising delay-dependen asympoically sable crieria only depend on e upper bound of e delay-derivaive and o e differenial-algebraic sysems e delay and is ime-derivaive dependen sabiliy crierion as no esablised wic moivaes is paper is aricle deals wi e problem of asympoic sabiliy for a class of linear differenial-algebraic sysem wi ime-varying delay e obained crieria depend no only on e upper bound bu also on e lower bound of e delay derivaive Based on e Lyapunov funcional meod and e delay pariioning approac some delay and is ime-derivaive dependen sable crieria are obained One numerical example is provided o demonsrae e effeciveness of e proposed resuls All e developed resuls are in e LMI framework wic makes em more ineresing since e soluions are easily obained using exising powerful ools like e LMI oolbox of Malab or any equivalen ool Noaion: rougou is paper A represens e ranspose of A; e symbol in marix inequaliy denoes e symmeric erm of e marix; A > ( < ) means A is a symmerical posiive (negaive) definie Sym M sands for M + M ; I is a uni marix marix; Problem Saemen Consider e following differenial-algebraic sysem: x R is e sae vecor e marix = + ( τ ) Ex Ax Ax () E R may be singular and we assume a τ is ime-varying delay were d d are consans e iniial con- were W is e space of absoluely coninuous n n n were rank ( E) = r n A and A are consan marices wi appropriae dimensions ( ) τ ( ) [ a b] a and i is assumed o saisfy d τ ( ) d diion is given by x( + θ) = φ( θ) θ [ b ] φ( θ) W n funcion φ : [ b ] R wi e square inegrable derivaive and wi e normal φ = φ( ) + φ( s) + φ( s) ds W b e following definiion lemmas and noaion are inroduced wic will be used in e proof of e main resuls Definiion ([6]) Sysem () is said o be regular if e caracerisic polynomial de ( se A) is no idenically zero ) Sysem () is said o be impulse-free if deg ( de ( se A) ) = rank ( E) Lemma ([4]) Le H F and G be real marices of appropriae dimensions en for any scalar ε > for all marices F saisfying F F I we ave: Main Resuls HFG + G F H εhh + ε G G d d P saisfying eorem Sysem () is asympoically sable for all differeniable delays τ ( ) [ a b] wi τ k if ere exis symmeric posiive-definie marices Q R ( ) S i i = S S S 5
3 H Liu Y C Ding k = ( k = ) and appropriaely dimensioned marices P j k E P P E ( ) P j Y j Y j Z j Z j j = j W and W suc a LMIs: < τ < for τ ( ) and τ ( ) and < τ > for τ ( ) and τ ( ) were τ ( ) = d d < τ < and < τ > are denoed in (8) and () respecively Proof e proof of is eorem is divided ino wo pars Firs we prove a e resuls wen τ ( ) < τ ( ) > and τ ( ) = respecively ensure a e derivaive of Lyapunov funcional is negaive Finally we prove e resuls given in e firs par ensure a sysem is regular and impulse-free Firs of all we divide e delay inerval [ a b] ino wo segmens: [ ] and [ ] were we denoe a + b = a = b and = en sysem () can be represened as Ex( ) = Ax( ) + χ[ ] Ax( ) [ ] ( ) τ + χ Ax τ were χ[ ] : R { } is e caracerisic funcion of [ ] if s [ ] χ[ ] ( s) () Consider e following Lyapunov funcional: were ( ) = ( τ ) V x x E P x V x = x s Qx s d s τ V x = x s Sx s s d = oerwise V x = V x + V x + V x + V x + V x () S S V4 ( x ) = ξ ( s) ξ( s) d s S 4 5 i ( ) = ( i+ i) ( ) i( ) V x Ex s R Ex s dd s θ 5 i= i + + θ ( ) S S = ξ s = x s x s Q > Ri > S > > S In addiion we define e coninuous funcion P( ( ) ) τ ( ) τ ( ) ( τ ) = χ[ ] ( τ ) + Wen τ as e following form: P P P τ one can obain ( ) τ ( ) τ + χ[ ] ( τ ( ) ) P + P ( P P ) ( χ)( P P ) χ P ( τ ( ) ) = τ ( ) + ( ) τ ( ) ( ) τ ( ) V τ ( x ) = x ( ) E P ( τ ( ) ) x( ) + x ( ) χ P + P τ + ( χ ) + P P Ex (4) 6
4 H Liu Y C Ding i V 5( x) = ( Ex ( ) ) ( i+ i) Ri( Ex ( ) ) ( i+ i) ( Ex ( s) ) Ri( Ex ( s) ) ds i + i= i= o obain e main resuls we consider e following ree cases: τ ( ) [ ) ( ) ( ] ( ) Case : τ ( ) [ ) j Using e fac a f ( s ) d s τ f j j j ( s ) d s d f s s = + j were f j ( s) ( Ex ( s) ) Ri( Ex ( s) ) τ = j+ j+ τ easily obain e following inequaliies by Jensen s inequaliy: i i i ( i+ i) i ( ) i ( ) f s ds Ex s dsr Ex s d s i+ i+ i+ ( ) ( ) + + j τ τ f s d s τ υ Rυ j j j j j j j j j ( ) ( + ) ( + )( + ) j+ ds υ j were υ j = ( Ex ( s) ) τ ( ) τ ( ) j derivaive of ( ) f s d s τ υ Rυ j j j j j j j j j j = V x along e soluion of () is given by τ ( ) Ex ( s) ds j j τ + + V x V x Ex R Ex τ < τ < i= ( ) = ( ) + ( ) ( i+ i) i ( ) ( τ ) ( τ ) ( τ ) x Qx x Qx + x Sx x Sx + ( ) ( ) x S S x + x S x x x x x x x E R E x x x x E R E x x τ υ υ S S ( ) S ( ) ( ) ( ) ( ) j j+ j jrj j τ υ υ ( + )( + ) R j j j j j j Leing η ( ) = x Ex x x υ υ x τ x following erms o (5) gives τ and = we i = j = en e ime- ( ) ( ) ( ) (5) and adding e = x Y + x E Y + x τ Ex + Ex τ + τ υ ( ) ( ) = x Z + x E Z + x W Ex Ex τ + τ υ ( τ ) (6) = x P + x E P Ax + Ax Ex for some scalar α > if V x η η α x (7) τ < τ < 7
5 H Liu Y C Ding were Π Π Π ZE Π5 Π6 Π7 Π YE ZE Π5 Π6 Π7 Π S E Π Π = τ < < Π55 Π57 Π Π Π Π ( ) τ τ Π = ( ) + ( ) EW ( ) E P P Sym P A τ + Sym P A + S E RE+ AP + P A Π = P + AP Π = E RE Y E ( τ ) ( τ ) Π = Y Π = Z 5 6 ( ) τ ( ) τ Π = PA+ PA+ Y E Z E+ P A 7 P P ( i+ i) Ri 5 ( τ ( ) ) Y i= Π = + Π = ( τ ) Π = Z Π = Y E Z E+ P A 6 7 Π = Q S + S E R E Π = S + S E R E 44 ( τ ) Π = S + E RE+ EW Π = R ( τ ) ( τ ) Π = Π = R ( τ ) ( τ ) Π = W Π = Q+ E+ E (8) Π = 88 S E RE Inequaliy (8) conains wo variables wic make i difficul o solve by LMI ool In order o overcome is difficuly we seek e sufficien condiions for inequaliy (8) Wen τ ( ) and τ ( ) e inequaliy (8) leads o e following LMIs: and Π Π Π ZE Z Π7 Π YE ZE Z Π7 Π S E = Π44 Π48 < ( ) R ( ) W Π77 EW Π88 (9) 8
6 H Liu Y C Ding were Πˆ Π Π ZE Y Πˆ 7 Π YE ZE Y Π7 Π S E 44 = Π Π48 < ( ) R ( ) Π77 EW Π 88 Π =Π Π =Π Π ˆ =Π Π ˆ =Π τ( ) = 7 7 τ( ) = τ( ) = 7 7 τ( ) = () Noe a we ave omied e zero row and zero column in and Leing ( ) ( ) ji η i = x Ex x x υ x τ x e laer wo LMIs imply (8) wic is because ( ) ( ) x τ τ η ( ) η ( ) + η η τ < = η η α is convex in ( ) [ ) us τ τ < τ = d i follows from (9) a Wen i e LMI () implies (9) since = < = i ( ) i τ = d () τ i d τ d + = < d d d d us τ d d Similarly we can obain a τ d d Case : τ ( ) ( ] By e definiion of e caracerisic funcion χ = we apply e above argumens and represenaions wi i = and j = In addiion we replace (6) wi e following equaions: is convex in [ ] ( τ ) ( ) ( τ ) ( τ ) υ = x Y + x E Y + x + x W Ex + Ex + ( ) ( ) is also convex in [ ] = x Z + x E Z Ex Ex τ + τ υ ( τ ) = + + x P x E P Ax Ax Ex and leing η ( ) ( ) = x Ex x x υ υ x τ x obain a for some scala α > were V x x η η α τ > τ > I is easy o 9
7 H Liu Y C Ding were Π Π E RE Y E Π 5 Π 6 Π 7 ZE Π YE Π 5 Π 6 Π 7 ZE Π Π 4 Π 5 W E Π 44 E S = < τ > Π 55 Π 57 Π 66 Π 77 S ( ) τ τ Π = ( ) + ( ) ( ) E P P P A Sym τ + Sym P A + S E RE+ AP + P A ( τ ) ( τ ) Π = P + AP Π = Y Π = Z 5 6 τ τ Π = P A P A Y E ZE P A P P ( i+ i) Ri 5 ( τ ( ) ) Y i= Π = + Π = ( τ ) Π = Z Π = Y E Z E+ P A 6 7 Π = Q S + S E R + R E Π = E RE W E+ S 4 ( τ ) Π = W Π = S + S E RE 5 44 ( τ ) ( τ ) Π = R Π = ( τ ) ( τ ) Π = R Π = Q+ E+ E () Similar o e case I we obain e resuls wen τ ( ) and ( ) < and < respecively Furer we can verify τ ( ) > is convex in ( ) ( ] are also convex in τ ( ) [ d d ] From Case and Case we ave [ ] ( ) [ ] ( ) τ wic can be marked as τ and χ τ η η + χ τ η η α τ τ < τ > () V x for some scalar α > τ = Case : { η η η η } α max τ τ τ (4) V x ( ) = ( ) < ( ) > erefore V ( x ) α x( ) wen τ ( ) [ ] τ ( ) [ d d ] a b Now e asympoic sabiliy of sysem () can no be obained ye since e exisence and uniqueness of a soluion o sysem () are no always guaraneed and e sysem may ave undesired impulsive beavior In e following we will prove a e above-menioned resuls ensure e regular and impulse-free I follows form (8) a
8 H Liu Y C Ding Pre- and pos-muliplying (5) by Π Π S < Π ( i+ i) R i i= I A and I A ( ) respecively we obain ( ) τ τ τ ( ) + Sym + Sym < E P P P A P A E RE Since ranke = r n ere mus exis wo inverible marices G and H n n suc a ˆ I E = GEH = r Similar o (7) we define i i ˆ A A ˆ i i P P A = GAH = P G P H i i i A A = = = P P4 i E P = P E i can be sown a P = Pre- and pos-muliplying (6) by k k en using H we can formulae e following inequaliy easily < Sym ( A ( P + P )) 4 4 were will be irrelevan o e following discussion Form (8) we ge A ( P P ) 4 4 (5) (6) (7) H and Sym + < and us A is nonsingular wic implies a de ( se A) is no idenically zero and deg ( de ( se A) ) = r = rank E Hence by Definiion e above-menioned resuls guaranee sysem () is regular and impulse-free is complees e proof Wen e marix E is nonsingular e resul in is case can be obained by seing E equal o I wi e appropriae ransformaions e corresponding resul is given by e following corollary: Corollary Sysem () wi E I τ a b wi k d τ ( ) d if ere exis symmeric posiive-definie marices Q Ri ( i = ) S S S S P ( k = ) and appropriaely dimensioned marices P j P j Y j Y j Z j Z j j ( j = ) W and W suc a LMIs: < τ < for τ ( ) and τ ( ) and < τ > for τ ( ) and τ ( ) were τ ( ) = d d = is asympoically sable for all differeniable delays [ ] < τ < and < τ > are denoed in (8) and () respecively k Wen d is unknown le P = P ( k = ) and τ ( ) = d we ave e following corollary Corollary Sysem () is asympoically sable for all differeniable delays τ ( ) [ a b] wi τ ( ) d if ere exis symmeric posiive-definie marices Q R i ( i = ) S S S S P saisfying E P = P E and appropriaely dimensioned marices P j P j Y j Y j Z j Z j j ( j = ) W and W suc a LMIs: < τ < for τ ( ) and τ ( ) and < τ > for τ ( ) and τ ( ) were τ ( ) = d < τ < and < τ > are denoed in (8) and () respecively Remark I sould be poined ou a if a is big enoug delay pariioning of [ a ] may improve e N > resuls In addiion e beer resuls may be obained if we divide e delay inerval [ ] ino N segmens 4 A Numerical Example In is secion a numerical example will be presened o sow e validiy of e main resuls derived above Example Consider e following linear differenial-algebraic sysem described by sysems () wi 5 5 E = A A = = a b (8)
9 H Liu Y C Ding For a = coosing d = and d = 9 and applying eorem e maximum values of b is 57 wic guaranees a e sysem is asympoically sable 5 Conclusion In is paper e asympoic sabiliy of differenial-algebraic sysem wi ime-varying delay as been invesigaed Some delay and is ime-derivaive dependen asympoically sable crieria ave been obained by decomposing ime-varying delay in a convex se e obained crieria depend no only on e upper bu also on e lower bound of e delay derivaive One numerical example as been given o illusrae e effeciveness of e proposed main resuls Acknowledgemens We ank e Edior and e referee for eir commens is work was suppored by A Projec Suppored by Scienific Researc Fund of Sicuan Provincial Educaion Deparmen (6ZA46) and e Docoral Researc Foundaion of Souwes Universiy of Science and ecnology (zx74) References [] Lin C Wang QG and Lee H (5) Robus Normalizaion and Sabilizaion of Uncerain Descripor Sysems wi Norm-Bounded Perurbaions IEEE ransacions on Auomaic Conrol p://dxdoiorg/9/ac [] Xu SY and Lam J (6) Robus Conrol and Filering of Singular Sysems Springer-Verlag Berlin [] Dai L (989) Singular Conrol Sysems Lecure Noes in Conrol and Informaion Sciences Springer-Verlag New York [4] Boukas EK (9) Delay-Dependen Robus Sabilizabiliy of Singular Linear Sysems wi Delays Socasic Analysis and Applicaions p://dxdoiorg/8/ [5] Cou JH Cen SH and Zang QL (6) Robus Conrollabiliy for Linear Uncerain Descripor Sysems Linear Algebra and is Applicaions p://dxdoiorg/6/jlaa55 [6] Haidar A and Boukas EK (9) Exponenial Sabiliy of Singular Sysems wi Muliple ime-varying Delays Auomaica p://dxdoiorg/6/jauomaica889 [7] Lu RQ Xu Y and Xue AK () H filering for Singular Sysems wi Communicaion Delays Signal Process p://dxdoiorg/6/jsigpro97 [8] Virnik E (8) Sabiliy Analysis of Posiive Descripor Sysems Linear Algebra and Is Applicaions p://dxdoiorg/6/jlaa8 [9] Wo SL Zou Y Cen QW and Xu SY (9) Non-Fragile Conroller Design for Discree Descripor Sysems Journal of e Franklin Insiue p://dxdoiorg/6/jjfranklin978 [] Long SH and Zong SM (6) H Conrol for a Class of Discree-ime Singular Sysems via Dynamic Feedback Conroller Applied Maemaics Leers 58-8 p://dxdoiorg/6/jaml64 [] Niamsup P and Pa VN (6) A New Resul on Finie-ime Conrol of Singular Linear ime-delay Sysems Applied Maemaics Leers 6-7 p://dxdoiorg/6/jaml65 [] Deng SJ Liao XF and Guo S (9) Asympoic Sabiliy Analysis of Cerain Neural Differenial Equaions: A Descripor Sysem Approac Maemaics and Compuers in Simulaion p://dxdoiorg/6/jmacom95 [] Qian W Liu J Sun YX and Fei SM () A Less Conservaive Robus Sabiliy Crieria for Uncerain Neural Sysems wi Mixed Delays Maemaics and Compuers in Simulaion p://dxdoiorg/6/jmacom97 [4] Xu SY Lam J and Yang C () Robus H Conrol for Discree Singular Sysems wi Sae Delay and Parameer Uncerainy Dynamics of Coninuous Discree and Impulsive Sysems [5] Yang CY Zang QL and Zou LN (7) Srongly Absolue Sabiliy of Lur e ype Differenial-Algebraic Sysems Journal of Maemaical Analysis and Applicaions p://dxdoiorg/6/jjmaa767 [6] Xu SY Van Dooren P Sefan R and Lam J () Robus Sabiliy and Sabilizaion for Singular Sysems wi Sae Delay and Parameer Uncerainy IEEE ransacions on Auomaic Conrol 47-8 p://dxdoiorg/9/ac865
10 H Liu Y C Ding [7] Fridman E () Sabiliy of Linear Descripor Sysems wi Delay: A Lyapunov Based Approac Journal of Maemaical Analysis and Applicaions p://dxdoiorg/6/s-47x()- [8] Park P and Ko JW (7) Sabiliy and Robus Sabiliy for Sysems wi a ime-varying Delay Auomaica p://dxdoiorg/6/jauomaica7 [9] Han QL (9) A Discree Delay Decomposiion Approac o Sabiliy of Linear Rearded and Neural Sysems Auomaica p://dxdoiorg/6/jauomaica885 [] Fridman E Saked U and Liu K (9) New Condiions for Delay-Derivaive-Dependen Sabiliy Auomaica p://dxdoiorg/6/jauomaica98 Submi your manuscrip a: p://papersubmissionscirporg/
A DELAY-DEPENDENT STABILITY CRITERIA FOR T-S FUZZY SYSTEM WITH TIME-DELAYS
A DELAY-DEPENDENT STABILITY CRITERIA FOR T-S FUZZY SYSTEM WITH TIME-DELAYS Xinping Guan ;1 Fenglei Li Cailian Chen Insiue of Elecrical Engineering, Yanshan Universiy, Qinhuangdao, 066004, China. Deparmen
More informationOn Robust Stability of Uncertain Neutral Systems with Discrete and Distributed Delays
009 American Conrol Conference Hya Regency Riverfron S. Louis MO USA June 0-009 FrC09.5 On Robus Sabiliy of Uncerain Neural Sysems wih Discree and Disribued Delays Jian Sun Jie Chen G.P. Liu Senior Member
More informationMean-square Stability Control for Networked Systems with Stochastic Time Delay
JOURNAL OF SIMULAION VOL. 5 NO. May 7 Mean-square Sabiliy Conrol for Newored Sysems wih Sochasic ime Delay YAO Hejun YUAN Fushun School of Mahemaics and Saisics Anyang Normal Universiy Anyang Henan. 455
More informationMethod For Solving Fuzzy Integro-Differential Equation By Using Fuzzy Laplace Transformation
INERNAIONAL JOURNAL OF SCIENIFIC & ECHNOLOGY RESEARCH VOLUME 3 ISSUE 5 May 4 ISSN 77-866 Meod For Solving Fuzzy Inegro-Differenial Equaion By Using Fuzzy Laplace ransformaion Manmoan Das Danji alukdar
More informationHigher Order Difference Schemes for Heat Equation
Available a p://pvau.edu/aa Appl. Appl. Ma. ISSN: 9-966 Vol., Issue (Deceber 009), pp. 6 7 (Previously, Vol., No. ) Applicaions and Applied Maeaics: An Inernaional Journal (AAM) Higer Order Difference
More informationStability and Bifurcation in a Neural Network Model with Two Delays
Inernaional Mahemaical Forum, Vol. 6, 11, no. 35, 175-1731 Sabiliy and Bifurcaion in a Neural Nework Model wih Two Delays GuangPing Hu and XiaoLing Li School of Mahemaics and Physics, Nanjing Universiy
More informationFuzzy Laplace Transforms for Derivatives of Higher Orders
Maemaical Teory and Modeling ISSN -58 (Paper) ISSN 5-5 (Online) Vol, No, 1 wwwiiseorg Fuzzy Laplace Transforms for Derivaives of Higer Orders Absrac Amal K Haydar 1 *and Hawrra F Moammad Ali 1 College
More informationResearch Article Further Stability Analysis of Time-Delay Systems with Nonlinear Perturbations
Hindawi Mahemaical Problems in Engineering Volume 7, Aricle ID 594757, pages hps://doi.org/.55/7/594757 Research Aricle Furher Sabiliy Analysis of Time-Delay Sysems wih Nonlinear Perurbaions Jie Sun andjingzhang,3
More informationNovel robust stability criteria of neutral-type bidirectional associative memory neural networks
www.ijcsi.org 0 Novel robus sabiliy crieria of neural-ype bidirecional associaive memory neural neworks Shu-Lian Zhang and Yu-Li Zhang School of Science Dalian Jiaoong Universiy Dalian 608 P. R. China
More informationRobust Stability and Stabilization for Singular Systems With State Delay and Parameter Uncertainty
11 IEEE RANSACIONS ON AUOMAIC CONROL, VOL. 47, NO. 7, JULY Now, we choose 8= 1; ; 1 9= 19; 5 5; 7 he corresponding Riccai equaion (13) admis he maximal soluion 5= 1; ; 7 : By heorem 2, all opimal conrols
More informationLecture 20: Riccati Equations and Least Squares Feedback Control
34-5 LINEAR SYSTEMS Lecure : Riccai Equaions and Leas Squares Feedback Conrol 5.6.4 Sae Feedback via Riccai Equaions A recursive approach in generaing he marix-valued funcion W ( ) equaion for i for he
More informationOn two general nonlocal differential equations problems of fractional orders
Malaya Journal of Maemaik, Vol. 6, No. 3, 478-482, 28 ps://doi.org/.26637/mjm63/3 On wo general nonlocal differenial equaions problems of fracional orders Abd El-Salam S. A. * and Gaafar F. M.2 Absrac
More informationA DELAY-DEPENDENT APPROACH TO ROBUST STABILITY FOR UNCERTAIN STOCHASTIC NEURAL NETWORKS WITH TIME-VARYING DELAY
Journal of Marine Science and echnology Vol. 8 No. pp. 77-83 (00) 77 A DELAY-DEPENDEN APPROACH O ROBUS SABILIY FOR UNCERAIN SOCHASIC NEURAL NEWORKS WIH IME-VARYING DELAY Chien-Yu Lu* Chin-Wen Liao* Koan-Yuh
More informationBifurcation Analysis of a Stage-Structured Prey-Predator System with Discrete and Continuous Delays
Applied Mahemaics 4 59-64 hp://dx.doi.org/.46/am..4744 Published Online July (hp://www.scirp.org/ournal/am) Bifurcaion Analysis of a Sage-Srucured Prey-Predaor Sysem wih Discree and Coninuous Delays Shunyi
More informationThe Asymptotic Behavior of Nonoscillatory Solutions of Some Nonlinear Dynamic Equations on Time Scales
Advances in Dynamical Sysems and Applicaions. ISSN 0973-5321 Volume 1 Number 1 (2006, pp. 103 112 c Research India Publicaions hp://www.ripublicaion.com/adsa.hm The Asympoic Behavior of Nonoscillaory Soluions
More informationSTABILITY OF NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS
Elecronic Journal of Differenial Equaions, Vol. 217 217, No. 118, pp. 1 14. ISSN: 172-6691. URL: hp://ejde.mah.xsae.edu or hp://ejde.mah.un.edu STABILITY OF NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
More informationPOSITIVE AND MONOTONE SYSTEMS IN A PARTIALLY ORDERED SPACE
Urainian Mahemaical Journal, Vol. 55, No. 2, 2003 POSITIVE AND MONOTONE SYSTEMS IN A PARTIALLY ORDERED SPACE A. G. Mazo UDC 517.983.27 We invesigae properies of posiive and monoone differenial sysems wih
More informationOrdinary Differential Equations
Ordinary Differenial Equaions 5. Examples of linear differenial equaions and heir applicaions We consider some examples of sysems of linear differenial equaions wih consan coefficiens y = a y +... + a
More informationRecursive Least-Squares Fixed-Interval Smoother Using Covariance Information based on Innovation Approach in Linear Continuous Stochastic Systems
8 Froniers in Signal Processing, Vol. 1, No. 1, July 217 hps://dx.doi.org/1.2266/fsp.217.112 Recursive Leas-Squares Fixed-Inerval Smooher Using Covariance Informaion based on Innovaion Approach in Linear
More information10. State Space Methods
. Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he
More informationThe L p -Version of the Generalized Bohl Perron Principle for Vector Equations with Infinite Delay
Advances in Dynamical Sysems and Applicaions ISSN 973-5321, Volume 6, Number 2, pp. 177 184 (211) hp://campus.ms.edu/adsa The L p -Version of he Generalized Bohl Perron Principle for Vecor Equaions wih
More informationResearch Article Modified Function Projective Synchronization between Different Dimension Fractional-Order Chaotic Systems
Absrac and Applied Analysis Volume 212, Aricle ID 862989, 12 pages doi:1.1155/212/862989 Research Aricle Modified Funcion Projecive Synchronizaion beween Differen Dimension Fracional-Order Chaoic Sysems
More informationCONTRIBUTION TO IMPULSIVE EQUATIONS
European Scienific Journal Sepember 214 /SPECIAL/ ediion Vol.3 ISSN: 1857 7881 (Prin) e - ISSN 1857-7431 CONTRIBUTION TO IMPULSIVE EQUATIONS Berrabah Faima Zohra, MA Universiy of sidi bel abbes/ Algeria
More informationOn Gronwall s Type Integral Inequalities with Singular Kernels
Filoma 31:4 (217), 141 149 DOI 1.2298/FIL17441A Published by Faculy of Sciences and Mahemaics, Universiy of Niš, Serbia Available a: hp://www.pmf.ni.ac.rs/filoma On Gronwall s Type Inegral Inequaliies
More informationPOSITIVE SOLUTIONS OF NEUTRAL DELAY DIFFERENTIAL EQUATION
Novi Sad J. Mah. Vol. 32, No. 2, 2002, 95-108 95 POSITIVE SOLUTIONS OF NEUTRAL DELAY DIFFERENTIAL EQUATION Hajnalka Péics 1, János Karsai 2 Absrac. We consider he scalar nonauonomous neural delay differenial
More informationSliding Mode Extremum Seeking Control for Linear Quadratic Dynamic Game
Sliding Mode Exremum Seeking Conrol for Linear Quadraic Dynamic Game Yaodong Pan and Ümi Özgüner ITS Research Group, AIST Tsukuba Eas Namiki --, Tsukuba-shi,Ibaraki-ken 5-856, Japan e-mail: pan.yaodong@ais.go.jp
More informationChapter 6. Systems of First Order Linear Differential Equations
Chaper 6 Sysems of Firs Order Linear Differenial Equaions We will only discuss firs order sysems However higher order sysems may be made ino firs order sysems by a rick shown below We will have a sligh
More informationApproximating the Powers with Large Exponents and Bases Close to Unit, and the Associated Sequence of Nested Limits
In. J. Conemp. Ma. Sciences Vol. 6 211 no. 43 2135-2145 Approximaing e Powers wi Large Exponens and Bases Close o Uni and e Associaed Sequence of Nesed Limis Vio Lampre Universiy of Ljubljana Slovenia
More informationAdditional Exercises for Chapter What is the slope-intercept form of the equation of the line given by 3x + 5y + 2 = 0?
ddiional Eercises for Caper 5 bou Lines, Slopes, and Tangen Lines 39. Find an equaion for e line roug e wo poins (, 7) and (5, ). 4. Wa is e slope-inercep form of e equaion of e line given by 3 + 5y +
More informationEXISTENCE OF NON-OSCILLATORY SOLUTIONS TO FIRST-ORDER NEUTRAL DIFFERENTIAL EQUATIONS
Elecronic Journal of Differenial Equaions, Vol. 206 (206, No. 39, pp.. ISSN: 072-669. URL: hp://ejde.mah.xsae.edu or hp://ejde.mah.un.edu fp ejde.mah.xsae.edu EXISTENCE OF NON-OSCILLATORY SOLUTIONS TO
More informationOn a Fractional Stochastic Landau-Ginzburg Equation
Applied Mahemaical Sciences, Vol. 4, 1, no. 7, 317-35 On a Fracional Sochasic Landau-Ginzburg Equaion Nguyen Tien Dung Deparmen of Mahemaics, FPT Universiy 15B Pham Hung Sree, Hanoi, Vienam dungn@fp.edu.vn
More informationA Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients
mahemaics Aricle A Noe on he Equivalence of Fracional Relaxaion Equaions o Differenial Equaions wih Varying Coefficiens Francesco Mainardi Deparmen of Physics and Asronomy, Universiy of Bologna, and he
More informationarxiv: v1 [math.gm] 4 Nov 2018
Unpredicable Soluions of Linear Differenial Equaions Mara Akhme 1,, Mehme Onur Fen 2, Madina Tleubergenova 3,4, Akylbek Zhamanshin 3,4 1 Deparmen of Mahemaics, Middle Eas Technical Universiy, 06800, Ankara,
More informationHamilton- J acobi Equation: Weak S olution We continue the study of the Hamilton-Jacobi equation:
M ah 5 7 Fall 9 L ecure O c. 4, 9 ) Hamilon- J acobi Equaion: Weak S oluion We coninue he sudy of he Hamilon-Jacobi equaion: We have shown ha u + H D u) = R n, ) ; u = g R n { = }. ). In general we canno
More information4. Advanced Stability Theory
Applied Nonlinear Conrol Nguyen an ien - 4 4 Advanced Sabiliy heory he objecive of his chaper is o presen sabiliy analysis for non-auonomous sysems 41 Conceps of Sabiliy for Non-Auonomous Sysems Equilibrium
More informationAsymmetry and Leverage in Conditional Volatility Models
Economerics 04,, 45-50; doi:0.3390/economerics03045 OPEN ACCESS economerics ISSN 5-46 www.mdpi.com/journal/economerics Aricle Asymmery and Leverage in Condiional Volailiy Models Micael McAleer,,3,4 Deparmen
More informationODEs II, Lecture 1: Homogeneous Linear Systems - I. Mike Raugh 1. March 8, 2004
ODEs II, Lecure : Homogeneous Linear Sysems - I Mike Raugh March 8, 4 Inroducion. In he firs lecure we discussed a sysem of linear ODEs for modeling he excreion of lead from he human body, saw how o ransform
More informationStatic Output Feedback Sliding Mode Control for Nonlinear Systems with Delay
AMSE JOURNALS 04-Series: Avances C; Vol. 69; N ; pp 8-38 Submie July 03; Revise April 5, 04; Accepe May, 04 Saic Oupu Feeback Sliing Moe Conrol for Nonlinear Sysems wih Delay H. Yao, F. Yuan School of
More informationResearch Article Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations
Hindawi Publishing Corporaion Boundary Value Problems Volume 11, Aricle ID 19156, 11 pages doi:1.1155/11/19156 Research Aricle Exisence and Uniqueness of Periodic Soluion for Nonlinear Second-Order Ordinary
More informationRobust estimation based on the first- and third-moment restrictions of the power transformation model
h Inernaional Congress on Modelling and Simulaion, Adelaide, Ausralia, 6 December 3 www.mssanz.org.au/modsim3 Robus esimaion based on he firs- and hird-momen resricions of he power ransformaion Nawaa,
More informationAsymmetry and Leverage in Conditional Volatility Models*
Asymmery and Leverage in Condiional Volailiy Models* Micael McAleer Deparmen of Quaniaive Finance Naional Tsing Hua Universiy Taiwan and Economeric Insiue Erasmus Scool of Economics Erasmus Universiy Roerdam
More informationAsymptotic instability of nonlinear differential equations
Elecronic Journal of Differenial Equaions, Vol. 1997(1997), No. 16, pp. 1 7. ISSN: 172-6691. URL: hp://ejde.mah.sw.edu or hp://ejde.mah.un.edu fp (login: fp) 147.26.13.11 or 129.12.3.113 Asympoic insabiliy
More informationSliding Mode Controller for Unstable Systems
S. SIVARAMAKRISHNAN e al., Sliding Mode Conroller for Unsable Sysems, Chem. Biochem. Eng. Q. 22 (1) 41 47 (28) 41 Sliding Mode Conroller for Unsable Sysems S. Sivaramakrishnan, A. K. Tangirala, and M.
More informationSUFFICIENT CONDITIONS FOR EXISTENCE SOLUTION OF LINEAR TWO-POINT BOUNDARY PROBLEM IN MINIMIZATION OF QUADRATIC FUNCTIONAL
HE PUBLISHING HOUSE PROCEEDINGS OF HE ROMANIAN ACADEMY, Series A, OF HE ROMANIAN ACADEMY Volume, Number 4/200, pp 287 293 SUFFICIEN CONDIIONS FOR EXISENCE SOLUION OF LINEAR WO-POIN BOUNDARY PROBLEM IN
More informationChapter 2. First Order Scalar Equations
Chaper. Firs Order Scalar Equaions We sar our sudy of differenial equaions in he same way he pioneers in his field did. We show paricular echniques o solve paricular ypes of firs order differenial equaions.
More informationd 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
More information(1) (2) Differentiation of (1) and then substitution of (3) leads to. Therefore, we will simply consider the second-order linear system given by (4)
Phase Plane Analysis of Linear Sysems Adaped from Applied Nonlinear Conrol by Sloine and Li The general form of a linear second-order sysem is a c b d From and b bc d a Differeniaion of and hen subsiuion
More informationA New Perturbative Approach in Nonlinear Singularity Analysis
Journal of Mahemaics and Saisics 7 (: 49-54, ISSN 549-644 Science Publicaions A New Perurbaive Approach in Nonlinear Singulariy Analysis Ta-Leung Yee Deparmen of Mahemaics and Informaion Technology, The
More informationThe Quantum Theory of Atoms and Molecules: The Schrodinger equation. Hilary Term 2008 Dr Grant Ritchie
e Quanum eory of Aoms and Molecules: e Scrodinger equaion Hilary erm 008 Dr Gran Ricie An equaion for maer waves? De Broglie posulaed a every paricles as an associaed wave of waveleng: / p Wave naure of
More informationResearch Article Dual Synchronization of Fractional-Order Chaotic Systems via a Linear Controller
The Scienific World Journal Volume 213, Aricle ID 159194, 6 pages hp://dx.doi.org/1155/213/159194 Research Aricle Dual Synchronizaion of Fracional-Order Chaoic Sysems via a Linear Conroller Jian Xiao,
More informationû s L u t 0 s a ; i.e., û s 0
Te Hille-Yosida Teorem We ave seen a wen e absrac IVP is uniquely solvable en e soluion operaor defines a semigroup of bounded operaors. We ave no ye discussed e condiions under wic e IVP is uniquely solvable.
More informationVariational Iteration Method for Solving System of Fractional Order Ordinary Differential Equations
IOSR Journal of Mahemaics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 1, Issue 6 Ver. II (Nov - Dec. 214), PP 48-54 Variaional Ieraion Mehod for Solving Sysem of Fracional Order Ordinary Differenial
More informationOpen Access Finite-time Stabilization for a Class of Networked Systems with Delay
Send Orders for Reprins o reprins@benhamscience.ae The Open Auomaion and Conrol Sysems Journal, 214, 6, 1779-1784 1779 Open Access Finie-ime Sabilizaion for a Class of Neworked Sysems wih Delay Hejun Yao
More informationAnti-Disturbance Control for Multiple Disturbances
Workshop a 3 ACC Ani-Disurbance Conrol for Muliple Disurbances Lei Guo (lguo@buaa.edu.cn) Naional Key Laboraory on Science and Technology on Aircraf Conrol, Beihang Universiy, Beijing, 9, P.R. China. Presened
More informationResearch Article Convergence of Variational Iteration Method for Second-Order Delay Differential Equations
Applied Mahemaics Volume 23, Aricle ID 63467, 9 pages hp://dx.doi.org/.55/23/63467 Research Aricle Convergence of Variaional Ieraion Mehod for Second-Order Delay Differenial Equaions Hongliang Liu, Aiguo
More informationOn Oscillation of a Generalized Logistic Equation with Several Delays
Journal of Mahemaical Analysis and Applicaions 253, 389 45 (21) doi:1.16/jmaa.2.714, available online a hp://www.idealibrary.com on On Oscillaion of a Generalized Logisic Equaion wih Several Delays Leonid
More informationt 2 B F x,t n dsdt t u x,t dxdt
Evoluion Equaions For 0, fixed, le U U0, where U denoes a bounded open se in R n.suppose ha U is filled wih a maerial in which a conaminan is being ranspored by various means including diffusion and convecion.
More informationStatic Output Feedback Variable Structure Control for a Class of Time-delay Systems
AMSE JOURNALS 04-Series: Avances C; Vol. 69; N ; pp 58-68 Submie Sep. 03; Revise June 30, 04; Accepe July 5, 04 Saic Oupu Feeback Variable Srucure Conrol for a Class of ime-elay Sysems Y. ian, H. Yao,
More informationChapter 3 Boundary Value Problem
Chaper 3 Boundary Value Problem A boundary value problem (BVP) is a problem, ypically an ODE or a PDE, which has values assigned on he physical boundary of he domain in which he problem is specified. Le
More informationStochastic Reliability Analysis of Two Identical Cold Standby Units with Geometric Failure & Repair Rates
DOI: 0.545/mjis.07.500 Socasic Reliabiliy Analysis of Two Idenical Cold Sandby Unis wi Geomeric Failure & Repair Raes NITIN BHARDWAJ AND BHUPENDER PARASHAR Email: niinbardwaj@jssaen.ac.in; parasar_b@jssaen.ac.in
More informationCERTAIN CLASSES OF SOLUTIONS OF LAGERSTROM EQUATIONS
SARAJEVO JOURNAL OF MATHEMATICS Vol.10 (22 (2014, 67 76 DOI: 10.5644/SJM.10.1.09 CERTAIN CLASSES OF SOLUTIONS OF LAGERSTROM EQUATIONS ALMA OMERSPAHIĆ AND VAHIDIN HADŽIABDIĆ Absrac. This paper presens sufficien
More informationTO our knowledge, most exciting results on the existence
IAENG Inernaional Journal of Applied Mahemaics, 42:, IJAM_42 2 Exisence and Uniqueness of a Periodic Soluion for hird-order Delay Differenial Equaion wih wo Deviaing Argumens A. M. A. Abou-El-Ela, A. I.
More informationComparison between the Discrete and Continuous Time Models
Comparison beween e Discree and Coninuous Time Models D. Sulsky June 21, 2012 1 Discree o Coninuous Recall e discree ime model Î = AIS Ŝ = S Î. Tese equaions ell us ow e populaion canges from one day o
More informationAnn. Funct. Anal. 2 (2011), no. 2, A nnals of F unctional A nalysis ISSN: (electronic) URL:
Ann. Func. Anal. 2 2011, no. 2, 34 41 A nnals of F uncional A nalysis ISSN: 2008-8752 elecronic URL: www.emis.de/journals/afa/ CLASSIFICAION OF POSIIVE SOLUIONS OF NONLINEAR SYSEMS OF VOLERRA INEGRAL EQUAIONS
More informationIMPROVED HYPERBOLIC FUNCTION METHOD AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT BENJAMIN-BONA-MAHONY-BURGERS EQUATION
THERMAL SCIENCE, Year 015, Vol. 19, No. 4, pp. 1183-1187 1183 IMPROVED HYPERBOLIC FUNCTION METHOD AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT BENJAMIN-BONA-MAHONY-BURGERS EQUATION by Hong-Cai MA a,b*,
More informationBoundedness and Exponential Asymptotic Stability in Dynamical Systems with Applications to Nonlinear Differential Equations with Unbounded Terms
Advances in Dynamical Sysems and Applicaions. ISSN 0973-531 Volume Number 1 007, pp. 107 11 Research India Publicaions hp://www.ripublicaion.com/adsa.hm Boundedness and Exponenial Asympoic Sabiliy in Dynamical
More informationGlobal Synchronization of Directed Networks with Fast Switching Topologies
Commun. Theor. Phys. (Beijing, China) 52 (2009) pp. 1019 1924 c Chinese Physical Sociey and IOP Publishing Ld Vol. 52, No. 6, December 15, 2009 Global Synchronizaion of Direced Neworks wih Fas Swiching
More informationRobust Finite-Time H Filtering for Itô Stochastic Systems
Journal o Applied Mahemaics and Physics, 26, 4, 75-7 hp://www.scirp.org/journal/jamp ISSN Online: 227-479 ISSN Prin: 227-452 Robus Finie-ime H Filering or Iô Sochasic Sysems Aiqing Zhang College o Mahemaics
More informationProperties Of Solutions To A Generalized Liénard Equation With Forcing Term
Applied Mahemaics E-Noes, 8(28), 4-44 c ISSN 67-25 Available free a mirror sies of hp://www.mah.nhu.edu.w/ amen/ Properies Of Soluions To A Generalized Liénard Equaion Wih Forcing Term Allan Kroopnick
More informationSTATE-SPACE MODELLING. A mass balance across the tank gives:
B. Lennox and N.F. Thornhill, 9, Sae Space Modelling, IChemE Process Managemen and Conrol Subjec Group Newsleer STE-SPACE MODELLING Inroducion: Over he pas decade or so here has been an ever increasing
More informationDISCRETE GRONWALL LEMMA AND APPLICATIONS
DISCRETE GRONWALL LEMMA AND APPLICATIONS JOHN M. HOLTE MAA NORTH CENTRAL SECTION MEETING AT UND 24 OCTOBER 29 Gronwall s lemma saes an inequaliy ha is useful in he heory of differenial equaions. Here is
More informationA Necessary and Sufficient Condition for the Solutions of a Functional Differential Equation to Be Oscillatory or Tend to Zero
JOURNAL OF MAEMAICAL ANALYSIS AND APPLICAIONS 24, 7887 1997 ARICLE NO. AY965143 A Necessary and Sufficien Condiion for he Soluions of a Funcional Differenial Equaion o Be Oscillaory or end o Zero Piambar
More informationHeat kernel and Harnack inequality on Riemannian manifolds
Hea kernel and Harnack inequaliy on Riemannian manifolds Alexander Grigor yan UHK 11/02/2014 onens 1 Laplace operaor and hea kernel 1 2 Uniform Faber-Krahn inequaliy 3 3 Gaussian upper bounds 4 4 ean-value
More informationCorrespondence should be addressed to Nguyen Buong,
Hindawi Publishing Corporaion Fixed Poin Theory and Applicaions Volume 011, Aricle ID 76859, 10 pages doi:101155/011/76859 Research Aricle An Implici Ieraion Mehod for Variaional Inequaliies over he Se
More informationt is a basis for the solution space to this system, then the matrix having these solutions as columns, t x 1 t, x 2 t,... x n t x 2 t...
Mah 228- Fri Mar 24 5.6 Marix exponenials and linear sysems: The analogy beween firs order sysems of linear differenial equaions (Chaper 5) and scalar linear differenial equaions (Chaper ) is much sronger
More informationExistence of non-oscillatory solutions of a kind of first-order neutral differential equation
MATHEMATICA COMMUNICATIONS 151 Mah. Commun. 22(2017), 151 164 Exisence of non-oscillaory soluions of a kind of firs-order neural differenial equaion Fanchao Kong Deparmen of Mahemaics, Hunan Normal Universiy,
More informationMath 315: Linear Algebra Solutions to Assignment 6
Mah 35: Linear Algebra s o Assignmen 6 # Which of he following ses of vecors are bases for R 2? {2,, 3, }, {4,, 7, 8}, {,,, 3}, {3, 9, 4, 2}. Explain your answer. To generae he whole R 2, wo linearly independen
More informationFractional Method of Characteristics for Fractional Partial Differential Equations
Fracional Mehod of Characerisics for Fracional Parial Differenial Equaions Guo-cheng Wu* Modern Teile Insiue, Donghua Universiy, 188 Yan-an ilu Road, Shanghai 51, PR China Absrac The mehod of characerisics
More informationExistence Theory of Second Order Random Differential Equations
Global Journal of Mahemaical Sciences: Theory and Pracical. ISSN 974-32 Volume 4, Number 3 (22), pp. 33-3 Inernaional Research Publicaion House hp://www.irphouse.com Exisence Theory of Second Order Random
More informationObserver design for a class of wave equation driven by an unknown periodic input
Milano (Ialy) Augus 8 - Sepember, 11 Observer design for a class of wave equaion driven by an unknown periodic inpu Jonaan Cauvin Absrac: In is paper, exponenially convergen observers are designed for
More informationOn the Separation Theorem of Stochastic Systems in the Case Of Continuous Observation Channels with Memory
Journal of Physics: Conference eries PAPER OPEN ACCE On he eparaion heorem of ochasic ysems in he Case Of Coninuous Observaion Channels wih Memory o cie his aricle: V Rozhova e al 15 J. Phys.: Conf. er.
More informationEvaluation of Mean Time to System Failure of a Repairable 3-out-of-4 System with Online Preventive Maintenance
American Journal of Applied Mahemaics and Saisics, 0, Vol., No., 9- Available online a hp://pubs.sciepub.com/ajams/// Science and Educaion Publishing DOI:0.69/ajams--- Evaluaion of Mean Time o Sysem Failure
More informationSettling Time Design and Parameter Tuning Methods for Finite-Time P-PI Control
Journal of Conrol Science an Engineering (6) - oi:.765/8-/6.. D DAVID PUBLISHING Seling ime Design an Parameer uning Mehos for Finie-ime P-PI Conrol Keigo Hiruma, Hisaazu Naamura an Yasuyui Saoh. Deparmen
More informationStabilization of NCSs: Asynchronous Partial Transfer Approach
25 American Conrol Conference June 8-, 25 Porland, OR, USA WeC3 Sabilizaion of NCSs: Asynchronous Parial Transfer Approach Guangming Xie, Long Wang Absrac In his paper, a framework for sabilizaion of neworked
More informationAn Introduction to Malliavin calculus and its applications
An Inroducion o Malliavin calculus and is applicaions Lecure 5: Smoohness of he densiy and Hörmander s heorem David Nualar Deparmen of Mahemaics Kansas Universiy Universiy of Wyoming Summer School 214
More informationRobust Control Over a Packet-based Network
Robus Conrol Over a Packe-based Nework Ling Shi, Michael Epsein and Richard M. Murray Absrac In his paper, we consider a robus nework conrol problem. We consider linear unsable and uncerain discree ime
More informationdi Bernardo, M. (1995). A purely adaptive controller to synchronize and control chaotic systems.
di ernardo, M. (995). A purely adapive conroller o synchronize and conrol chaoic sysems. hps://doi.org/.6/375-96(96)8-x Early version, also known as pre-prin Link o published version (if available):.6/375-96(96)8-x
More informationPade and Laguerre Approximations Applied. to the Active Queue Management Model. of Internet Protocol
Applied Mahemaical Sciences, Vol. 7, 013, no. 16, 663-673 HIKARI Ld, www.m-hikari.com hp://dx.doi.org/10.1988/ams.013.39499 Pade and Laguerre Approximaions Applied o he Acive Queue Managemen Model of Inerne
More informationFinish reading Chapter 2 of Spivak, rereading earlier sections as necessary. handout and fill in some missing details!
MAT 257, Handou 6: Ocober 7-2, 20. I. Assignmen. Finish reading Chaper 2 of Spiva, rereading earlier secions as necessary. handou and fill in some missing deails! II. Higher derivaives. Also, read his
More informationCourse Notes for EE227C (Spring 2018): Convex Optimization and Approximation
Course Noes for EE7C Spring 018: Convex Opimizaion and Approximaion Insrucor: Moriz Hard Email: hard+ee7c@berkeley.edu Graduae Insrucor: Max Simchowiz Email: msimchow+ee7c@berkeley.edu Ocober 15, 018 3
More informationResearch Article The Effect of Initial State Error for Nonlinear Systems with Delay via Iterative Learning Control
Hindawi Publishing Corporaion Advances in Mahemaical Physics Volume 216, Aricle ID 461945, 6 pages hp://dx.doi.org/1.1155/216/461945 Research Aricle The Effec of Iniial Sae Error for Nonlinear Sysems wih
More informationApplication of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing
Applicaion of a Sochasic-Fuzzy Approach o Modeling Opimal Discree Time Dynamical Sysems by Using Large Scale Daa Processing AA WALASZE-BABISZEWSA Deparmen of Compuer Engineering Opole Universiy of Technology
More informationThe motions of the celt on a horizontal plane with viscous friction
The h Join Inernaional Conference on Mulibody Sysem Dynamics June 8, 18, Lisboa, Porugal The moions of he cel on a horizonal plane wih viscous fricion Maria A. Munisyna 1 1 Moscow Insiue of Physics and
More informationY 0.4Y 0.45Y Y to a proper ARMA specification.
HG Jan 04 ECON 50 Exercises II - 0 Feb 04 (wih answers Exercise. Read secion 8 in lecure noes 3 (LN3 on he common facor problem in ARMA-processes. Consider he following process Y 0.4Y 0.45Y 0.5 ( where
More information( ) ( ) if t = t. It must satisfy the identity. So, bulkiness of the unit impulse (hyper)function is equal to 1. The defining characteristic is
UNIT IMPULSE RESPONSE, UNIT STEP RESPONSE, STABILITY. Uni impulse funcion (Dirac dela funcion, dela funcion) rigorously defined is no sricly a funcion, bu disribuion (or measure), precise reamen requires
More informationSumudu Decomposition Method for Solving Fractional Delay Differential Equations
vol. 1 (2017), Aricle ID 101268, 13 pages doi:10.11131/2017/101268 AgiAl Publishing House hp://www.agialpress.com/ Research Aricle Sumudu Decomposiion Mehod for Solving Fracional Delay Differenial Equaions
More informationStability Analysis of Network Controlled Temperature Control System with Additive Delays
Copyrigh ech Science Press CMES, vol.4, no., pp.-4, Sabiliy Analysis of Nework Conrolled emperaure Conrol Sysem wih Addiive Delays V. Venkaachalam, * and D. Prabhakaran Absrac: his paper presens, using
More informationOn external semi-global stochastic stabilization of linear systems with input saturation
1 On exernal semi-global sochasic sabilizaion of linear sysems wih inpu sauraion Anon A. Soorvogel 1,AliSaberi 2 and Siep Weiland 3 Absrac This paper inroduces he noion of exernal semi-global sochasic
More informationExistence of positive solution for a third-order three-point BVP with sign-changing Green s function
Elecronic Journal of Qualiaive Theory of Differenial Equaions 13, No. 3, 1-11; hp://www.mah.u-szeged.hu/ejqde/ Exisence of posiive soluion for a hird-order hree-poin BVP wih sign-changing Green s funcion
More informationLAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
More information