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Stability Analysis for Systems with Impulse Effects
Authors:Jianhua Shen  Zhujun Jing
Institution:(1) Department of Mathematics, College of Huaihua, Huaihua, Hunan, 418008, P. R. China;(2) Department of Mathematics, Hunan Normal University, Changsha, Hunan, 410081, P. R. China;(3) Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, P. R. China
Abstract:In the present paper the authors establish new conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulsive effects described by systems of nonlinear, time-varying ordinary differential equations. For the case when the corresponding systems without impulsive effects admit unstable properties, the above results are used to establish conditions under which the uniform stability even uniform asymptotic stability of equilibria of systems with impulsive effects can be caused by impulsive perturbations . 1991 Mathematics Subject Classification. 34D 20, 34K 20.
Keywords:hybrid dynamical systems  lyapunov stability  systems with impulses
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