中文摘要：

针对一类具有多重状态时滞和凸多面体不确定性的离散切换系统．研究该系统在任意切换信号下基于状态观测器的输出反馈鲁棒镇定问题。首先通过状态变量的替换将多时滞项转变成不含时滞项，再利用分段Lyapunov函数和线性矩阵不等式方法，导出凸多面体不确定多时滞离散切换系统基于观测器的输出反馈鲁棒镇定的充分条件，并将此条件转化成为一组线性矩阵不等式的可行性问题，同时给出基于状态观测器的输出反馈控制器。仿真结果表明设计方法是可行有效的。

英文摘要：

Under arbitrary switching signals, the observer-based output feedback robust stabilization is studied for a class of switched discrete-time systems with polytopic uncertainties and multi-delays in states. Firstly, the state variables with time delays are substituted for one state vector without any time delays, Secondly, based on the piecewise quadratic Lyapunov functions and linear matrix inequali- ty （LM1） method, the sufficient condition is derived for the observer based output feedback robust stabilization. Then the feasibility problem is convent to the LMIs constraint problem. And the synthesis method of the output feedback controllers is developed. The simu- lation results verify the effectiveness of the proposed approach.