Invariance Principles for Nonlinear Discrete-Time Switched Systems and Its Application to Output Synchronization of Dynamical Networks
基于多重李雅普诺夫函数和弱李雅普诺夫函数，为非线性离散时间切换系统建立了两个不变性原理，并应用于具有非相同节点的动态网络输出同步。
In this article, we develop two invariance principles for nonlinear discrete-time switched systems based on multiple Lyapunov functions and multiple weak Lyapunov functions, respectively, which allow the first differences of multiple weak Lyapunov functions to be positive on certain sets. It is shown that the solution of the system is attracted to the largest weakly invariant set in a certain specific region. Then, based on the invariance principle developed and geometrical dissipativity, we obtain the generalized output synchronization for discrete-time dynamical networks with nonidentical nodes by an appropriate switching among several communication topologies. Finally, two examples are provided to demonstrate the effectiveness of the main results.