基于LMI的离散时滞切换系统反馈镇定

针对一类子系统为离散时滞系统的切换系统，提出了一种系统稳定性与反馈镇定的控制方法.通过状态变量的转换，将时滞切换系统变为不含时滞项的切换系统.在系统中增加等式约束，将具有双线性矩阵不等式（BMI）形式的综合问题转换为线性矩阵不等式（LMI）的凸优化问题.在任意切换信号作用下离散线性切换系统渐近稳定理论基础上，以线性矩阵不等式形式给出了离散时滞切换系统渐近稳定的充分性条件，并且给出了切换系统状态反馈镇定和输出反馈镇定的控制器设计方法.两个数值算例结果表明，所设计控制方法是可行的，在控制方法的作用下，闭环系统是渐近稳定的.

Feedback stabilization based on linear matrix inequalities for discrete switched systems with time-delay

Aimed at discrete switched systems with time-delay subsystems,a method was proposed to analyze the system stability and feedback stabilization.Switched systems with time-delay were converted into switched systems without time-delay by state vector transformation.The synthesis problem in the form of bilinear matrix inequalities(BMI) was transferred into convex optimal problem in the form of linear matrix inequalities(LMI) by adding equation constraint in the systems. Based on the asymptotic stability theory under arbitrary switching signals for discrete linear switched systems,the sufficient condition for asymptotic stability of discrete switched systems with time delay was given in the form of LMI.A state feedback stabilization method and an output feedback stabilization method were designed respectively.Two illustrative example results show that the method is feasible,and that the closed-loop system under the proposed method is asymptotically stabile.