Razumikhin–Lyapunov functional method for the stability of impulsive switched systems with time delay

This paper investigates the uniform stability and the uniform asymptotical stability of impulsive switched systems with time delay. By employing the method of Razumikhin–Lyapunov functional, several Razumikhin-type theorems of uniform stability and uniform asymptotical stability are established, whi...

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Bibliographic Details
Published in:Mathematical and computer modelling 2009, Vol.49 (1), p.249-264
Main Authors: Liu, Yubin, Feng, Weizhen
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Lyapunov functional
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Ordinary differential equations
Razumikhin technique
Sciences and techniques of general use
Switched systems
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Uniform asymptotical stability
Uniform stability
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Summary:This paper investigates the uniform stability and the uniform asymptotical stability of impulsive switched systems with time delay. By employing the method of Razumikhin–Lyapunov functional, several Razumikhin-type theorems of uniform stability and uniform asymptotical stability are established, which improve some of the existing results. Several examples are also given to illustrate the results.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2008.01.004