Exponential stability of impulsive delayed linear differential equations

Authors:
Jin Zhou;Quanjun Wu
Affiliations:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China
Venue:
IEEE Transactions on Circuits and Systems II: Express Briefs
Year:
2009

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Abstract

This brief considers the global exponential stability of impulsive delayed linear differential equations. By utilizing the Lyapunov function methods combined with the Razumikhin technique, several criteria on exponential stability are analytically derived, which are substantially an extension and a generalization of the corresponding results in recent literature. Compared with some existing works, a distinctive feature of this brief is to address exponential stability problems for any fixed-time delays. It is shown that the delayed linear differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. An example and its simulation are also given to illustrate the theoretic results.