不确定切换奇异时滞系统鲁棒指数容许性分析

讨论一类连续时间不确定切换奇异区间时变时滞系统的鲁棒指数容许性问题. 通过定义衰减率依赖李亚普诺夫函数并利用平均驻留时间法, 给出一个时滞区间依赖充分条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 本文获得的结论为连续时间切换奇异时滞系统的基本问题提供了一个解, 即识别切换信号使得切换奇异时滞系统正则、无脉冲且均方指数稳定. 数值例子说明本文结果的有效性.

Robust Exponential Admissibility of Uncertain Switched Singular Time-delay Systems

This paper investigates the problem of robust exponential admissibility for a class of continuous-time uncertain switched singular systems with interval time-varying delay. By defining a properly constructed decay-rate-dependent Lyapunov function and the average dwell time approach, a delay-range-dependent sufficient condition is derived for the nominal system to be regular, impulse free, and exponentially stable. This condition is also extended to uncertain case. The obtained results provide a solution to one of the basic problems in continuous-time switched singular time-delay systems, that is, to identify a switching signal for which the switched singular time-delay system is regular, impulse free, and exponentially stable. Numerical examples are given to demonstrate the effectiveness of the obtained results.