转移概率部分未知的时滞不确定Markov跳跃系统稳定性分析

Stability analysis of delayed Markovian jumping systems with uncertainty and partial information on transition probabilities

研究转移概率部分未知的时滞不确定的Markov跳跃系统随机稳定性问题,基于Lyapunov稳定理论,构造合适的Lyapunov泛函,使用自由权矩阵技术和凸结合技术来估计积分项的上界,同时也充分考虑时滞下界和上界的关系,得到保证Markov跳跃系统随机稳定性的充分性条件,该条件以线性矩阵不等式的形式表示。最后,数值例子和其仿真验证了所提方法的有效性和优越性。

This paper focused on the stability problems of delayed Markovian jumping systems with uncertainty and partial information on transition probabilities. Based on Lyapunov stability theory, it constructed proper Lyapunov functional, and used free-weighting matrix technique and convex combination technique to estimate the upper of the integral terms. It derived some sufficient conditions to guarantee that the Markovian jumping systems were stochastic stability in terms of linear matrix inequalities, in which the relationship between the lower and the upper of delay were fully taken into account. Finally, a numerical example and its simulation verify the effectiveness and superiority of the proposed method.