Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods

被引：131
作者：
Dashkovskiy, Sergey [2 ]
Kosmykov, Michael [1 ]
Mironchenko, Andrii [1 ]
Naujok, Lars [1 ]
机构：
[1] Univ Bremen, Ctr Ind Math, D-28334 Bremen, Germany
[2] Univ Appl Sci Erfurt, Dept Civil Engn, Erfurt, Germany
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2012年 / 6卷 / 03期
关键词：
Impulsive systems; Large-scale systems; Lyapunov methods; Input-to-state stability; Time delays; SMALL-GAIN THEOREM; TO-STATE STABILITY; NETWORKED CONTROL-SYSTEMS; ISS SYSTEMS; DIFFERENTIAL EQUATIONS; HYBRID SYSTEMS; STABILIZATION;
D O I：
10.1016/j.nahs.2012.02.001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider the input-to-state stability (ISS) of impulsive control systems with and without time delays. We prove that, if the time-delay system possesses an exponential Lyapunov-Razumikhin function or an exponential Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time delays and prove that the whole network is uniformly ISS under the small-gain and the average dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems, a Lyapunov-Krasovskii functional or a Lyapunov-Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples. (c) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：899 / 915
页数：17
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