不确定时滞Lur′e系统的非脆弱保性能控制  

Non-fragile guarantee cost control for uncertain Lur′e systems with time-delay

作　　者：张佳成[1] 吴保卫[1] 李新芳[1] 

机构地区：[1]陕西师范大学数学与信息科学院,陕西西安710062

出　　处：《西北大学学报（自然科学版）》2009年第5期738-744,共7页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10571114);陕西省自然科学基础研究计划基金资助项目(SJ08A20)

摘　　要：目的设计一类不确定时滞Lur′e系统的非脆弱保性能控制器。方法针对非线性部分具有区间限制,而且具有不确定的Lur′e系统,将非脆弱控制器思想引入到这类系统之中,利用线性矩阵不等式(LM I)方法,研究被控对象和控制器同时存在扰动的非脆弱保性能问题。结果对于控制器存在加法扰动的情况,以线性矩阵不等式约束条件给出了Lur′e系统非脆弱保性能的充分条件,从而根据线性矩阵的可行性解给出了相应的控制器设计方法。特别地,还给出了一种寻找系统最小性能指标的方法,并用线性矩阵不等式工具箱求得其相应的最优保性能控制器。最后,数值算例说明此方法的可行性。结论推广了已有Lur′e系统的结果。Aim To design a non-fragile gurantee cost controller for a class of uncertain Lur＇e systems with timedelay. Methods The designation idea of non-fragile guaranteed cost controller is introduced to a class of uncertain Lur＇e system with time-delay and sector restricted nonlinearities. Based on linear matrix inequality （LMI） techniques, the problem of guaranteed cost control is addressed, where the uncertainties exist both in the systematic matrix and in the controller gain. Results Under the additive perturbation,the sufficient condition of nonfragile guaranteed cost is presented, and the corresponding controller design is given in terms of the feasible solutions of LMIs. Especially, the method of finding to illustrate the feasibility of the the minmum guaranteed cost of system was proposed. A numerical example is given to illustrate the feasibility of the designed method. Conclusion The results of predecessors are extended.

关 键 词：不确定性Lur′e系统 时滞 非脆弱控制器 保性能控制 线性矩阵不等式(LMI) 

分 类 号：O231[理学—运筹学与控制论]