多状态时变时滞的不确定系统的鲁棒H_∞控制器的设计

Design of Robust H_∞ Controller for Uncertain Systems with Multiple-States Time-Varying Delays

针对一类多状态时变时滞的不确定系统,采用求解Riccati不等式的方法,给出闭环系统二次稳定的一个充分条件.使用LMI方法研究了该系统H∞反馈控制器的分析与设计,给出系统无记忆二次能镇定且具有H∞性能的一个LMI条件,并通过对受条件约束的线性矩阵不等式的描述,给出系统存在γ-次优状态反馈H∞控制律的设计方法.利用Matlab工具箱给出一个算例,验证了设计方法的优越性和有效性.

This paper is concerned with the problem of analyzing and designing H∞ feedback controllers for a class of uncertain systems with multiple-states time-varying delays by using the LMI approach. A sufficient condition for the closed-loop system that is quadratically stable is presented by solving the Riccati inequality. In addition,a condition for the given systems with memoryless quadratically stabilizable and H∞ properties is presented in term of a certain linear matrix inequality,and the designing method of the Robust H∞ controllers is obtained by solving the LMI. Finally,an example is presented to illustrate the effectiveness and superiority of the design method by using Matlab tool box.