时滞半Markov切换随机系统输入–状态稳定性分析的时变驻留时间条件方法

本文针对时滞半Markov切换随机系统,建立了一种基于时变驻留时间条件的不定多重Lyapunov-Razumikhin函数方法,给出了系统输入–状态稳定性和积分输入–状态稳定性判别条件.一方面,构造了一种不定多重Lyapunov函数,不要求每个子系统对应的Lyapunov-Razumikhin函数导数总是保持负定,从而放宽了对于子系统稳定性要求,甚至允许了不稳定子系统的存在;另一方面,提出了一种时变驻留时间条件来表示半Markov切换信号的切换次数与子系统驻留时间之间的关系,利用时变函数对切换次数进行估计,间接放松了不定多重Lyapunov-Razumikhin函数选取的限制.最后,数值算例验证了所提方法的有效性.

Approach of time-varying dwell time condition for the input-to-state stability analysis of the time-delayed stochastic systems with semi-Markovian switching

The time-delayed stochastic systems with semi-Markovian switching are investigate in this paper. We establish an indefinite multiple Lyapunov-Razumikhin functions method based on a time-varying dwell time condition, and get input-to-state stability and integral input-to-state stability conditions. On the one hand, by introducing the indefinite multiple Lyapunov functions, we do not require that derivatives of Lyapunov-Razumikhin functions always remain negative, which eases stability requirements of subsystems, even allows unstable subsystems to exist. On the other hand, a time-varying dwell time condition is proposed to illustrate the connection between the switch counts and the dwell time. By this condition, we propose a time-varying functions to estimate the switch counts of the semi-Markovian switching signal, which mediately loosens the restrictions of multiple Lyapunov functions. Finally, a numerical example is presented to show the effectiveness of our results.