一类具有不稳定子系统的时滞切换非线性正系统指数稳定性

Exponential stability for a class of switched nonlinear positive systemswith partial unstable subsystems and time-delay

研究具有不稳定模态的时滞切换非线性正系统的指数稳定问题.首先,针对具有不稳定模态的时滞切换非线性正系统,基于改进的Halanay不等式技术结合多重最大分离Lyapunov函数,并设计模态依赖的切换策略,建立系统指数稳定的充分条件;其次,由于不再限制子系统运行的最小驻留时间,相比已有结果该条件的保守性更低,并且时滞切换线性正系统指数稳定作为该结果的特殊情况也被得到;最后,通过给定的数值实例展示理论结果的有效性.

This article investigates exponential stability problems of switched nonlinear positive systems(SNPSs)with partial unstable subsystems and time-delay.Firstly,based on improved Halanay inequality technique combined with multiple max-separable Lyapunov functions,and designing mode dependent average dwell time(MDADT)switching strategies,sufficient conditions of exponential stability of the SNPS are obtained.Then,the conservatism of stability conditions is lower than the previous results due to no restrictions on minimum dwell time of each subsystem,and exponential stability conditions of switched positive linear systems including time-delay,as the special cases,are concluded.Finally,a given example is shown to illustrate the effectiveness of theoretical results.