不确定随机多时滞系统鲁棒随机稳定性分析

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。

Robust stochastic stability for uncertain stochastic system with multiple delays

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 integral 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.