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

Iasson Karafyllis, Pierdomenico Pepe, Zhong-Ping Jiang

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)3339-3362
Number of pages24
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number7-8
DOIs
StatePublished - Oct 1 2009

Fingerprint

Functional Difference Equation
Retarded Functional Differential Equations
Difference equations
Differential equations
Convergence of numerical methods
Subsystem
Neutral Functional Differential Equation
Hyperbolic Partial Differential Equations
Interconnection
Differential System
Lyapunov
Partial differential equations
Large scale systems
Composite
Feedback
Output

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Stability results for systems described by coupled retarded functional differential equations and functional difference equations. / Karafyllis, Iasson; Pepe, Pierdomenico; Jiang, Zhong-Ping.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 71, No. 7-8, 01.10.2009, p. 3339-3362.

Research output: Contribution to journalArticle

@article{74a9fc5acd984bc383931ec1e0a7a99b,
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 Zhong-Ping Jiang",
year = "2009",
month = "10",
day = "1",
doi = "10.1016/j.na.2009.01.244",
language = "English (US)",
volume = "71",
pages = "3339--3362",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "7-8",

}

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

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

UR - http://www.scopus.com/inward/record.url?scp=67349201640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349201640&partnerID=8YFLogxK

U2 - 10.1016/j.na.2009.01.244

DO - 10.1016/j.na.2009.01.244

M3 - Article

VL - 71

SP - 3339

EP - 3362

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 7-8

ER -