Class- estimates and input-to-state stability analysis of impulsive switched systems

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• 作者：Jun Liu^a ; ^{j.liu@sheffield.ac.uk} ; Xinzhi Liu^b ; ^{xzliu@uwaterloo.ca} ; Wei-Chau Xie^c ; ^{xie@uwaterloo.ca}
• 关键词：Hybrid systems ; Input-to-state stability ; Stability in two measures ; Impulsive system ; Switched system
• 刊名：Systems and Control Letters
• 出版年：2012
• 期刊代码：171_01676911
• 类别：et
• 出版时间：June, 2012
• 卷：61
• 期：6
• 页码：738-746
• 文件大小：564 K

摘要

In this paper, we investigate input-to-state stability of impulsive switched systems. The goal is to bridge two apparently different, but both useful, stability notions, input-to-state stability and stability in terms of two measures, in the hybrid systems setting. Based on two class- function estimates and a comparison theorem for impulsive differential equations, two sets of sufficient Lyapunov-type conditions for input-to-state stability in terms of two measures are obtained for impulsive switched systems. These conditions exploit some nonlinear integral constraints in terms of generalized dwell-time conditions to balance the continuous dynamics and impulsive dynamics so that input-to-state stability is achieved, despite possible instability of individual continuous subsystems or destabilizing impulsive effects. An illustrative example is presented, together with numerical simulations, to demonstrate the main results.