不确定随机多时滞系统鲁棒随机稳定性分析  

Robust stochastic stability for uncertain stochastic system with multiple delays

作　　者：张慧慧[1] 夏建伟[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252000

出　　处：《山东大学学报（工学版）》2015年第1期54-63,共10页Journal of Shandong University（Engineering Science）

基　　金：国家自然科学基金资助项目(61004046;61104117)

摘　　要：研究了一类不确定随机多时滞系统的鲁棒随机稳定性问题,其中系统不确定参数满足线性分式结构。首先,将倒数凸方法加以推广,得到一个新的积分不等式引理;然后,充分考虑时滞区间上下限关系,构造了多时滞区间相关的李雅普诺夫函数,并在新的积分不等式方法下,得到具有更小保守性和较少自由变量的时滞相关稳定性条件;最后,给出一些数值仿真实例,验证了所提方法的有效性。The problem of robust stochastic stability for a class of uncertain stochastic systems with multiple delays was investigated in this paper. The uncertainties were in linear fractional form. Firstly, a new integral inequlity lemma was derived by extending the reciprocally convex approach. Then, based on a multiple delay-interval dependent Lyapunov- Krasovskii constructed by fully considering the relationship between upper and lower time delay interval and the new in- tegral inequlity approach, some novel delay-dependent stability criteria with less conservatism and less free weighting matrices were obtained. At last, some numerical examples were given to show the effectiveness of the proposed results.

关 键 词：随机系统 鲁棒随机稳定 线性结构不确定性 多时滞 李雅普诺夫函数 LMI 

分 类 号：O231.3[理学—运筹学与控制论]