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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, we discuss the finite time stability and state feedback control problems for a class of singular switched systems with continuous switching. First, we discuss the existence conditions of solutions for singular systems with continuous switching and then give the concepts of finite-time stability and finite-time boundedness for singular systems with continuous switching. Secondly, by using the model relying on the average dwell time method and the Lyapunov function method, sufficient conditions for switching singular systems to be regular, impulsive free and finite-time stable and finite-time bounded are given respectively. The state feedback controller is designed to make the closed-loop system finite Time-stable and finite-time-bounded and with H∞ performance index γ. Finally, a numerical example is given to verify the effectiveness of the proposed method.