网络上时滞相关脉冲非线性时滞耦合系统的积分输入到状态稳定性

The Integral Input-to-State Stability of Networked Delay-Related Impulse Nonlinear Time-Delay Coupling Systems

本文研究了网络上时滞相关脉冲的一般非线性时滞耦合系统的积分输入到状态稳定(iISS)性质。利用图论方法和Lyapunov-Krasovskii方法,在单个顶点系统iISS的Lyapunov函数的基础上,构造了整个网络iISS的Lyapunov函数,并推导出了网络上时滞相关脉冲的一般非线性时滞耦合系统存在iISS的充分条件。这些条件表明,如果每个节点上的连续时间系统都是iISS时,网络上时滞相关脉冲非线性时滞耦合系统在不稳定的脉冲出现的频率不太高的情况下仍能保证iISS的性质。

This paper investigates the integral-input-to-state stability (iISS) of general nonlinear delayed impulsive coupled systems on networks with delay-dependent impulses. With the assistance of graph theory and the Lyapunov-Krasovskii method, an iISS Lyapunov function for the total network is constructed based on the iISS Lyapunov functions of individual vertex systems, and sufficient conditions for iISS for general nonlinear delayed impulsive coupled systems on networks are derived. It is demonstrated that, when every continuous vertex system is iISS, the nonlinear delayed impulsive coupled systems on networks can still maintain iISS property provided the destabilizing impulses do not occur too frequently.