Exponential Stability of Impulsive Delayed Linear Differential Equations

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.