一类不确定奇异周期时变系统的鲁棒非脆弱_∞控制  

Robust and non-fragile H_∞ control for linear time-varying uncertain periodic singular systems with parameter uncertainty

作　　者：樊仲光[1,2] 梁家荣[3] 肖剑[4] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004 [2]河池学院教师教育学院,广西宜州546300 [3]广西大学计算机与电子信息学院,广西南宁530004 [4]华中科技大学控制科学与工程系,湖北武汉430074

出　　处：《山东大学学报（理学版）》2011年第1期20-27,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61064002);教育部“新世纪优秀人才支持计划”专项基金资助项目(NCET-06-0756)

摘　　要：对状态矩阵具有不确定性的奇异周期时变系统的鲁棒非脆弱H∞控制问题进行了研究。提出参数不确定性奇异周期时变系统广义可镇定和广义二次可镇定且具有H∞性能指标的概念,利用线性矩阵不等式方法,得到了一类参数不确定性奇异周期时变系统广义二次可镇定且具有H∞性能指标γ的一个充分条件,分别给出了相应的控制器增益具有加法式摄动和乘法式摄动的鲁棒非脆弱H∞状态反馈控制律的设计方法,所得的状态反馈控制律使得闭环系统正则、稳定、无脉冲,而且具有给定的H∞性能指标。最后,通过数值算例说明了该方法的有效性。The problem of robust and non-fragile H∞ control for a class of linear time-varying uncertain periodic singular systems with uncertainty in both the state matrix and matrices was studied. The concept of ＇ generalized stabilizability＇ and ＇ generalized quadratic stabilizability with H∞ performance index＇ for uncertain periodic singular systems were put forward. In terms of linear matrix inequalities, a sufficient condition for generalized quadratic stabilization with a H∞ performance index y was derived. The corresponding robust non-fragile H∞ state feedback controller with both additive perturbations and multiplicative perturbations was proposed such that the closed-loop system was regular, stable, and impulse free, as well as satisfying a prescribed H∞ performance index. Finally, a numerical example was presented to illustrate the validity of the approach.

关 键 词：不确定奇异周期时变系统 鲁棒非脆弱H∞控制 线性矩阵不等式 广义二次可镇定 加性和乘性摄动 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]