Lyapunov–Krasovskii functional for uniform stability of coupled differential-functional equations

This article discusses the Lyapunov–Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 45; no. 3; pp. 798 - 804
Main Authors: Gu, Keqin, Liu, Yi
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.03.2009
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Exact sciences and technology
Lyapunov–Krasovskii functional
Stability
System theory
Time delay
Lyapunov–Krasovskii functional
Stability
Time delay
Singularity
Differential equation
Functional equation
Delay system
Stability criterion
Difference equation
Modeling
Conservative system
Neutral system
Discretization
Linear matrix inequality
Lyapunov-Krasovskii functional
Delay time
Quadratic functional
Lyapunov function
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:This article discusses the Lyapunov–Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov–Krasovskii functional is established. Discretization is used to render the stability criterion to an LMI form.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2008.10.024