具有状态时滞的Markov切换系统的稳定条件  

Stability conditions for Markovian switching systems with state-delay

作　　者：盛遵冰[1] 陆磊 吕东方[1] 丛屾[1] 

机构地区：[1]黑龙江大学机电工程学院,哈尔滨150080 [2]烟台冰轮重型机件有限公司,山东烟台264006

出　　处：《黑龙江大学工程学报》2016年第1期79-86,共8页Journal of Engineering of Heilongjiang University

基　　金：国家自然科学基金资助项目(61573131);黑龙江省自然科学基金资助项目(LC201428)

摘　　要：考虑时滞Markov切换系统的均方指数稳定性分析。在不计及Brown运动的条件下,由于Markov切换系统仍然遵循Riemann-Lebesgue意义下的微积分法则。因此基于较为一般的Lyapunov-Krasovskii泛函构造方式,系统地推广了时滞系统稳定性研究中的解析方法与技巧。通过引入自由参数矩阵,建立了以线性矩阵不等式所表述的与时滞相关的稳定性判据,由此给出了均方指数稳定性的完整证明。仿真算例证实了方法的有效性。This note is concerned with the stability analysis in the mean square sense for Markovian switching systems with state-delay. The calculus rules in Riemann-Lebesgue sense are available for Markovian switching systems when the Brownian motion is not accounted. Then,based on the complete form of Lyapunov-Krasovskii functional,the existent methods and techniques for deterministic time-delay systems are generalized systematically.By introducing relaxation matrices,the delay-dependent stability criterion is estabilished in terms of linear matrix inequality,through which the exponential stability in the mean square is strictly verified. Numerical example demonstrates the proposed approach.

关 键 词：MARKOV切换系统 状态时滞 稳定性分析 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]