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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。
For a class of discrete switched systems with multiple state delays and convex polytopes, the output feedback robust stabilization of this system under arbitrary switching signals is studied. Firstly, the multi-delay term is transformed into a non-delay term by replacing the state variables. Then, by using the piecewise Lyapunov function and the linear matrix inequality method, the output feedback robust stabilization of the discrete-switched multi-delay system with convex polytopic is derived. Sufficient conditions, and transforms this condition into a feasible problem of a set of linear matrix inequalities. At the same time, an output feedback controller based on state observer is given. Simulation results show that the design method is feasible and effective.