A new approach to practical stability of impulsive functional differential equations in terms of two measures

In this work, we consider a new approach to the practical stability theory of impulsive functional differential equations. With Lyapunov functionals and Razumikhin technique, we use a new technique in the division of Lyapunov functions, given by Shunian Zhang, and obtain conditions sufficient for th...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2009, Vol.223 (1), p.449-458
Main Authors: Liu, Yang, Zhao, Shouwei
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Global analysis, analysis on manifolds
Impulsive functional differential equations
Lyapunov functions
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Practical stability
Razumikhin technique
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Wedge functions
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Summary:In this work, we consider a new approach to the practical stability theory of impulsive functional differential equations. With Lyapunov functionals and Razumikhin technique, we use a new technique in the division of Lyapunov functions, given by Shunian Zhang, and obtain conditions sufficient for the uniform practical (asymptotical) stability of impulsive delay differential equations. An example is also discussed to illustrate the advantage of the proposed results.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.01.029