Stability results for systems described by coupled retarded functional differential equations and functional difference equations

In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system can be regarded as the feedback interconnection of a subsyst...

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Vydáno v:Nonlinear analysis Ročník 71; číslo 7; s. 3339 - 3362
Hlavní autoři: Karafyllis, Iasson, Pepe, Pierdomenico, Jiang, Zhong-Ping
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Ltd 01.10.2009
Elsevier
Témata:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Input-to-Output Stability
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Small-gain theorem
Time-delay systems
Time-delay systems
Input-to-Output Stability
Small-gain theorem
Differential equation
Nonlinear analysis
Functional equation
Delay system
Difference equation
Mathematical model
Numerical stability
ISSN:0362-546X, 1873-5215
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Shrnutí:In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system can be regarded as the feedback interconnection of a subsystem described by RFDEs and a subsystem described by FDEs. Recent small-gain results and Lyapunov-like characterizations of the Weighted Input-to-Output Stability property for systems described by RFDEs and FDEs are employed. It is shown that the stability results provided in this work can be used to study stability for systems described by neutral functional differential equations and systems described by hyperbolic partial differential equations.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.01.244