时滞广义时变系统的容许性分析与镇定  

Admissibility and Stabilization for a Class of Time-Varying Linear Singular Systems with Time Delay

作　　者：苏晓明[1] 张启亮[1] 

机构地区：[1]沈阳工业大学理学院,辽宁沈阳110870

出　　处：《数学的实践与认识》2017年第14期305-312,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61074005);辽宁省高等教育基金(LR2012005)

摘　　要：研究了时滞广义时变系统的容许性与镇定性问题.首先,基于广义Lyapunov不等式、线性矩阵不等式和受限等价方法,建立时滞广义时变系统的Lyapunov不等式,将时滞广义时变系统的容许性问题转化为求解时滞广义时变系统的Lyapunov不等式问题,得到了系统容许的充分条件.然后,根据充分条件进一步研究了时滞广义时变系统的镇定问题,给出了状态反馈镇定器的设计方法.最后,通过数值算例验证了所得结论的有效性.This paper addresses the problems of admissibility and stabilization for timevarying linear singular systems with time delay. Firstly, based on the analysis method of singular Lyapunov inequality, linear matrix inequality and restrained equal transformation.A Lyapunov inequality for time-varying linear singular system with time delay is established. The problem of admissibility for time-varying linear singular system with time delay is transformed into solving the Lyapunov inequality for time-varying linear singular system with time delay problem. The sufficient condition of admissibility is obtained for the system. Furthermore, the class of the problem of stabilization is considered and presents a design method of state feedback stabilization. Finally, two numerical examples are given to illustrate the effectiveness of the approach.

关 键 词：时滞广义时变系统 Lyapunov不等式 线性矩阵不等式 容许性 

分 类 号：O231[理学—运筹学与控制论]