时滞矩形广义系统的混合H∞与无源控制  

Mixed H∞ and Passive Control for Stabilization for Time-Delay Rectangular Descriptor Systems

作　　者：黎婕 林崇[1] 刘焕霞 LI Jie;LIN Chong;LIU Huanxia(Institute of Complexity Science,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2020年第2期1-8,23,共9页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金资助项目(61673227,61873137)。

摘　　要：针对时滞矩形广义系统的混合H∞与无源控制问题,本文通过构造带时滞的动态补偿器,利用实数域上正常广义系统的可容许性判据,得到可使闭环系统在混合H∞与无源性能指标γ条件下容许的充分条件。通过构建合适的Lyapunov-Krasovskii泛函,结合放松过的Wirtinger不等式,对泛函导数积分项进行处理,将不等式中非线性项进行代换,最后通过数值算例验证该方法的有效性,并将混合H∞与无源控制问题从正常广义系统推广到时滞矩形广义系统。验证结果表明,本文所得到的稳定性充分条件拥有更大的时滞上界,决策变量更少,保守性和复杂度更低。该研究对时滞矩形广义系统的稳定性分析与控制器设计问题具有重要意义。Aiming at the problem of mixed H∞and passive control for time-delay rectangular descriptor systems,this paper constructs a dynamic compensator with time delay and uses the admissibility criterion of a normal singular system to obtain sufficient conditions under mixed H∞ and passive performance indexγrequirements.Firstly,a suitable Lyapunov-Krasovskii functional is constructed in this paper.Then,the derivative term of the functional derivative is processed in combination with the relaxed Wirtinger inequality,and then the non-linear term in the inequality is replaced.Finally,numerical example verifies the validity of the method.In this paper,the mixed H∞and passive control problem is extended from a normal singular system to a rectangular descriptor system with time delay.The verification results show that the method in this paper has a larger upper bound on time delay,fewer decision variables,and lower conservatism and complexity than the sufficient stability conditions obtained by the existing results.This research is of great significance to the stability analysis and controller design of rectangular descriptor systems with time delay.

关 键 词：矩形广义系统 混合H∞与无源控制 时滞 动态补偿 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] N941.1[自动化与计算机技术—控制科学与工程]