时滞状态反馈下离散时滞系统H_∞控制器失效时间分析

H-infinity controller failure time analysis for a class of discrete time-delay systems under delayed state feedback

针对控制器存在短暂失效的情形,研究一类时变时滞离散系统在时滞状态反馈控制下的H_∞控制器失效时间分析问题.本文的目标是寻求控制器正常工作时间与失效时间的比率应满足的条件以确保系统指数镇定且具有加权l_2增益.为此,基于切换的思想,所考虑的系统被转化为一个仅含有两个子系统的切换系统,其中一个子系统是控制器失效时的不稳定子系统,另一个是控制器未失效时的稳定子系统.通过使用多Lyapunov函数及平均驻留时间方法,给出问题可解的充分条件及时滞状态反馈H_∞切换控制器的设计方案.仿真算例表明了所得结果的有效性.

Based on the delayed state feedback strategy,this paper considers the H-infinity controller failure time analysis problem for a class of discrete time-varying delay systems in the presence of controller temporary failure.The main objective of this brief is to find the conditions of activation time ratio between the normal working time and the failure time of the controller,such that the considered systems are exponentially stabilizable and achieve a weighted l2--gain.To address this situation,the discrete time-varying delay systems subjected to controller temporary failure are converted into a class of discrete time-varying delay switched systems incorporating two subsystems,one subsystem is an unstable system without stabilizing controller,and the other subsystem is a stable system with stabilizing controller.By using piecewise Lyapunov function theory and average dwell-time method,sufficient conditions for the problem to be solvable are presented and a delayed state feedback H-infinity switching controller is designed in the form of linear matrix inequalities.Finally,a numerical example is given to illustrate the effectiveness of the proposed results.