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STABILITY ANALYSIS IN TERMS OF TWO MEASURES FOR IMPULSIVE DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  24 March 2003

CHUNHAI KOU ,
SHUNIAN ZHANG  and
SHUJIN WU
CHUNHAI KOU
Affiliation:
Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200240, Chinakouchunhai@263.net
SHUNIAN ZHANG
Affiliation:
Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200240, Chinakouchunhai@263.net
SHUJIN WU
Affiliation:
Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200240, Chinakouchunhai@263.net
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Abstract

Through the use of the so-called variational Lyapunov method, which is developed by combining the method of variation of parameters and the Lyapunov second method, stability and instability properties in terms of two measures for impulsive differential equations with variable moments of impulsive effects are discussed. Some stability and instability criteria are established. These theorems, together with an example, show that perturbation and impulsive effects may make a stable system uniformly asymptotically stable or unstable. These results significantly generalize the known ones.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 142 - 152
Copyright
The London Mathematical Society, 2002

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Footnotes

This work is supported by the NNSF of China (19831030).