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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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
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Abstract	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.
AbstractList	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.
Author	Jiang, Zhong-Ping Karafyllis, Iasson Pepe, Pierdomenico
Author_xml	– sequence: 1 givenname: Iasson surname: Karafyllis fullname: Karafyllis, Iasson email: ikarafyl@enveng.tuc.gr organization: Department of Environmental Engineering, Technical University of Crete, 73100, Chania, Greece – sequence: 2 givenname: Pierdomenico surname: Pepe fullname: Pepe, Pierdomenico email: pepe@ing.univaq.it organization: Dipartimento di Ingegneria Elettrica, Universita degli Studi dell’Aquila, Monteluco di Roio, 67040, L’Aquila, Italy – sequence: 3 givenname: Zhong-Ping surname: Jiang fullname: Jiang, Zhong-Ping email: zjiang@control.poly.edu organization: Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, NY 11201, USA
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Snippet	In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs)...
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SubjectTerms	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
Title	Stability results for systems described by coupled retarded functional differential equations and functional difference equations
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