中文摘要：

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.

英文摘要：

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.