基于推广的概率分布区间分解法的时滞系统稳定性分析

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.

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

Based on the generalized probability-distribution-interval decomposition, the problem of probability- distribution-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.