不确定时滞LPV系统的鲁棒稳定性分析  

Robust stability analysis of uncertain LPV systems with time delay

作　　者：刘玉忠[1] 李珊玉 LIU Yuzhong;LI Shanyu(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2020年第5期407-411,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅高等学校基本科研项目(LFW201712)。

摘　　要：研究了一类不确定时滞LPV系统的鲁棒稳定性问题,该类LPV系统在结构上存在不确定性。首先,通过构造一类限定时滞上界和时滞下界的李雅普诺夫泛函的方法,利用Schur补引理,对矩阵不等式进行处理,得到了系统鲁棒稳定的充分必要条件;其次,为了分析系统的鲁棒性能,引入一个二次型性能指标以及一个加权矩阵,得到系统鲁棒稳定并且满足性能指标的充分条件;最后,由于参数存在依赖性,使用近似基函数及网格技术的方法,将无限维的线性矩阵不等式(LMI)转化为有限维的线性矩阵不等式,把不确定时滞LPV系统的鲁棒稳定性问题归结为线性矩阵不等式的求解问题,从而可以方便地利用Matlab工具箱对其进行求解。The robust stability of a class of uncertain LPV systems with time-delay is studied.There is structural uncertainty in this kind of LPV systems.Firstly,by constructing a class of Lyapunov functional with finite upper bound and lower bound of time-delay,the sufficient and necessary conditions for the robust stability of the system are obtained by using the Schur complementary lemma.Secondly,in order to analyze the robust performance of the system,a quadratic performance index and a weighted matrix are introduced,and the sufficient conditions for the robust stability of the system and the performance index are obtained.Finally,due to the dependence of parameters,the infinite dimensional LMI is transformed into the finite dimensional LMI by using the method of approximate basis function and grid technology,and the robust stability problem of uncertain LPV systems with time delay is reduced to the solution of LMI,so that it can be easily solved by using Matlab toolbox.

关 键 词：不确定时滞LPV系统 鲁棒稳定性 性能指标 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]