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

Iasson Karafyllis; Pierdomenico Pepe; Zhong Ping Jiang

doi:10.1016/j.na.2009.01.244

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

Iasson Karafyllis, Pierdomenico Pepe, Zhong Ping Jiang

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	3339-3362
Number of pages	24
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
Issue number	7-8
DOIs	https://doi.org/10.1016/j.na.2009.01.244
State	Published - Oct 1 2009

Keywords

Input-to-Output Stability
Small-gain theorem
Time-delay systems

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2009.01.244

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title = "Stability results for systems described by coupled retarded functional differential equations and functional difference equations",

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.",

keywords = "Input-to-Output Stability, Small-gain theorem, Time-delay systems",

author = "Iasson Karafyllis and Pierdomenico Pepe and Jiang, {Zhong Ping}",

note = "Funding Information: The work of Z.-P. Jiang has been supported in part by NSF grants ECS-0093176, OISE-0408925 and DMS-0504462. The work of P. Pepe has been supported by the Italian MIUR Project PRIN 2005. ",

year = "2009",

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doi = "10.1016/j.na.2009.01.244",

language = "English (US)",

volume = "71",

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TY - JOUR

T1 - Stability results for systems described by coupled retarded functional differential equations and functional difference equations

AU - Karafyllis, Iasson

AU - Pepe, Pierdomenico

AU - Jiang, Zhong Ping

N1 - Funding Information: The work of Z.-P. Jiang has been supported in part by NSF grants ECS-0093176, OISE-0408925 and DMS-0504462. The work of P. Pepe has been supported by the Italian MIUR Project PRIN 2005.

PY - 2009/10/1

Y1 - 2009/10/1

N2 - 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.

AB - 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.

KW - Input-to-Output Stability

KW - Small-gain theorem

KW - Time-delay systems

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 7-8

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

Abstract

Keywords

ASJC Scopus subject areas

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