切换奇异系统的有限时间稳定

Finite-time stability for switched singular systems

本文研究了一类连续切换奇异系统的有限时间稳定和状态反馈控制问题.首先,讨论了连续切换奇异系统解的存在条件,然后给出连续切换奇异系统有限时间稳定和有限时间有界的概念;其次,利用模型依赖平均驻留时间方法和Lyapunov函数方法,分别给出切换奇异系统是正则、脉冲自由且有限时间稳定和有限时间有界的充分条件,并设计状态反馈控制器,使得闭环系统有限时间稳定和有限时间有界且具有H∞性能指标γ;最后通过数值算例验证了本文方法的有效性.

In this paper, finite-time stability and stabilization of switched singular systems are studied. Firstly, we discuss the solvability condition of the switched singular system and introduce the concepts of finite-time stability and finite- time boundness. Secondly, using the mode-dependent average dwell time method and the Lyapunov function method, we provide sufficient conditions to guarantee that the switched singular system is regular, impulse free, and finite-time stable or finite-time bounded. Then, we design the state feedback controllers to ensure that a closed-loop system is finite-time stable and finite-time bounded with a present H∞ disturbance attenuation level γ. Finally, numerical examples are given to verify the efficiency of the proposed theory.