随机时滞马尔可夫跳变非线性系统的鲁棒耗散控制  

Robust dissipative control for uncertain stochastic systems with Markovian switching and time-varying delay

作　　者：许莉娟[1] 张天平[1] 裔扬[1] 

机构地区：[1]扬州大学信息工程学院,扬州225009

出　　处：《东南大学学报（自然科学版）》2010年第S1期198-205,共8页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60874045,60904030);江苏省高校自然科学基础研究计划资助项目(09KJB510019);江苏省自然科学基金资助项目(BK2009184)

摘　　要：研究了Ittype不确定随机时滞马尔可夫跳变非线性系统的鲁棒耗散控制问题.该系统包含了Markov跳变参数、时变参数不确定性以及未知非线性函数,这些因素在实际中经常遇到且容易导致系统性能变差甚至不稳定.基于Lyapunov-Krasovskii函数的方法设计无记忆状态反馈耗散控制器,使得闭环系统对于所有容许的不确定性鲁棒随机稳定且严格(Q,S,R)-耗散.利用线性矩阵不等式形式给出了不确定随机马尔可夫跳变系统鲁棒随机稳定及严格(Q,S,R)-耗散问题可解的充分条件以及控制器的设计方法.最后,通过一个数值仿真验证了该方法的有效性.研究结果推广了现存的对于随机时滞马尔可夫跳变系统的H∞控制和无源控制的结论.This paper deals with the problem of robust dissipative control for a class of Ito^-typeuncertain stochastic jump systems with time-varying delay. The systems under studying are subject to Markov jump,time-varying parameter uncertainties,and unknown nonlinear functions,which are often encountered in practice and are also the sources of poor performance and instability. The statefeedback dissipative controller is designed on the basis of Lyapunov-Krasovskii functional approach such that,for all admissible uncertainties,the closed-loop system is robustly stochastically stable and strictly ( Q,S,R) -dissipative. Using the linear matrix inequality ( LMI) ,the sufficient condition on the existence of solution of these problems is given. And the design problem of state-feedback dissipative controller is converted to the problem of solving a set of linear matrix inequalities. Finally,a numerical example is provided to demonstrate the effectiveness of the proposed approach. The main results extend the existing results on H∞ control and passive control for stochastic time-delay jump systems.

关 键 词：Ito-type随机时滞系统 马尔可夫过程 鲁棒随机稳定 耗散控制 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]