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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Bibliographic Details
Published in:Nonlinear analysis Vol. 71; no. 7; pp. 3339 - 3362
Main Authors: Karafyllis, Iasson, Pepe, Pierdomenico, Jiang, Zhong-Ping
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.10.2009
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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