区间时变时滞Markov跳变系统的一种改进稳定性分析方法  

AN IMPROVED STABILITY ANALYSIS APPROACH FOR MARKOVIAN JUMP SYSTEMS WITH INTERVAL TIME-VARYING DELAYS

作　　者：黄玲[1] 孙敏[1] 

机构地区：[1]哈尔滨理工大学自动化学院,哈尔滨150080

出　　处：《系统科学与数学》2016年第7期995-1005,共11页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学青年基金(61304046)资助课题

摘　　要：采用一种新型的Lyapunov-Krasovskii泛函对线性时变时滞Markov跳变系统的稳定性进行研究.提出一种基于交叉项和积分项与标量函数乘积的新型增广LyapunovKrasovskii泛函.该函数中含有更多独立增广变量,有利于减小系统稳定性相对于时滞的保守性.利用二次凸组合、交叉项估计推导出系统随机渐近稳定时滞依赖的充分条件,并进一步求解线性矩阵不等式.数值算例说明所提方法的正确性和有效性.This paper deals with the problem for linear Markovian jump systems with interval time-varying delays, by using a novel Lyapunov-Krasovskii functional. Newly proposed augmented Lyapunov-Krasovskii functional are constructed by the cross-terms of variables and the quadratic terms multiplied by a scalar function. This functional may reduce conservativeness of delay-dependent stability since more independent augmented variables are introduced. A sufficient condition for the stochastic asymptotic stability of the system is derived by applying the ideas of second-order convex combination and the estimation of cross items. The obtained results are formulated in terms of linear matrix inequalities. A numerical example shows the validity and feasibility of the results.

关 键 词：MARKOV跳变系统 线性矩阵不等式 区间时变时滞 

分 类 号：O231[理学—运筹学与控制论]