采用一种新型的Lyapunov-Krasovskii泛函对线性时变时滞Markov跳变系统的稳定性进行研究. 提出一种基于交叉项和积分项与标量函数乘积的新型增广Lyapunov-Krasovskii泛函. 该函数中含有更多独立增广变量, 有利于减小系统稳定性相对于时滞的保守性. 利用二次凸组合、交叉项估计推导出系统随机渐近稳定时滞依赖的充分条件, 并进一步求解线性矩阵不等式. 数值算例说明所提方法的正确性和有效性.

This paper deals with the problem for linear Markovian jump systems with interval time-varying delays, by using a novel Lyapunov-Krasovskii functional. Newly proposed augmented Lyapunov-Krasovskii functional are constructed by the cross-terms of variables and the quadratic terms multiplied by a scalar function. This functional may reduce conservativeness of delay-dependent stability since more independent augmented variables are introduced. A sufficient condition for the stochastic asymptotic stability of the system is derived by applying the ideas of second-order convex combination and the estimation of cross items. The obtained results are formulated in terms of linear matrix inequalities. A numerical example shows the validity and feasibility of the results.