基于推广的概率分布区间分解法的时滞系统稳定性分析  

Stability analysis for delays systems based on generalized probability-distribution-interval decomposition approach

作　　者：刘健辰[1] 时光[1] LIU Jian-chen SHI Guang(Faculty of Electrical and Control Engineering, Liaoning Technical University, Huludao 125105, China)

机构地区：[1]辽宁工程技术大学电气与控制工程学院,辽宁葫芦岛125105

出　　处：《控制与决策》2017年第10期1824-1830,共7页Control and Decision

基　　金：国家自然科学基金项目(61304090);辽宁省教育厅科学研究一般项目(L2013130)

摘　　要：基于推广的概率分布区间分解法,研究一类具有随机时滞系统的概率分布相关稳定性问题.充分利用随机时滞的概率分布信息,获得一系列稳定性判据;通过严格的数学证明,表明通过增加概率区间数可以逐渐降低稳定性判据的保守性,从而建立一组新的分层结构LMI条件;严格证明了在采用相同概率区间划分的条件下,所得到的稳定性判据的保守性低于不考虑时滞概率分布的时变时滞分解法所得到的结果,并且分析和比较了两种方法的计算量.Based on the generalized probability-distribution-interval decomposition, the problem of probabilitydistribution-dependent stability analysis for a class of systems with stochastic delays is investigated. The information of the probability distribution of stochastic delay is fully employed and a series of sufficient stability criteria are obtained. It is illustrated by rigorous mathematical proof that the conservatism of the proposed stability criteria can be reduced progressively by increasing the number of the probability interval, which establishes a novel hierarchy of LMI conditions. It is rigorously proved that, with the same decomposition of probability interval, the conservatism of the proposed stability criteria is less than the one obtained by time-varying delay decomposition approach in which the probability-distribution of delay is ignored. The computation burden of the proposed method and the time-varying delay decomposition approach is analyzed and compared.

关 键 词：随机时滞系统 概率分布相关稳定性 概率分布区间分解 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]