具有两种滞量的不确定随机时滞系统的稳定性及鲁棒控制  

Stability and Robust Control for Uncertain Stochastic Time-delay System with Two Kinds of Delay

作　　者：潘超 王汝凉 庞健婵 PAN Chao;WANG Ru-liang;PANG Jian-chan(College of Mathematics and Statistics Nanning 530100,China;College of Physics and Electronics Nanning 530100,China;College of Computer and Information Engineering,Nanning Normal University,Nanning 530100,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530100 [2]南宁师范大学物理与电子工程学院,广西南宁530100 [3]南宁师范大学计算机与信息工程学院,广西南宁530100

出　　处：《南宁师范大学学报（自然科学版）》2021年第4期25-32,共8页Journal of Nanning Normal University：Natural Science Edition

基　　金：广西自然科学基金项目(2020GXNSFAA297184)。

摘　　要：研究了一类不确定随机时滞系统的稳定性以及鲁棒H∞控制性能γ问题.通过构造一个Lyapunov函数,结合Ito公式,用加减项和积分不等式的定理进行放缩得到一个二次型多项式,并构造出该式所对应矩阵,通过相关引理得出关于该类不确定随机时滞系统的随机渐近稳定性的条件,再在此系统基础上构造新的不确定随机时滞系统,运用类似的方法研究系统的H∞控制器设计问题,得出系统具有鲁棒H∞控制性能γ的条件,最后以数值算例验证了系统的可行性和有效性.The problem of stability and robust H∞ control performance γ for a class of stochastic time-delay system with uncertainty was investigated.By constructing a Lyapunov function,and combiningformulas to process functions,we use addition and subtraction terms and integral inequalities to scale.We also use the obtained quadratic polynomial to construct the corresponding matrix.The conditions are obtained for the stochastic asymptotic stability of this kind of uncertain stochastic time-delay system,and then a new uncertain stochastic time-delay system is constructed on the basis of this system.By using a similar method to study the design of the system controller,we can get the conditions for the robust H∞ control performanceγproblem.Finally,a numerical example is used to verify the conclusions obtained to ensure the feasibility of the system.

关 键 词：线性矩阵不等式(LMI) 不确定随机时滞系统 李雅普诺夫函数 

分 类 号：O212[理学—概率论与数理统计]