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  

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

作　　者：刘乾 何勇 宁重阳 LIU Qian;HE Yong;NING Chong-yang(School of Automation,China University of Geosciences,Wuhan Hubei 430074,China;Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems,Wuhan Hubei 430074,China;School of Computer and Information Engineering,Central South University of Forestry and Technology,Changsha Hunan 410004,China)

机构地区：[1]中国地质大学(武汉)自动化学院,湖北武汉430074 [2]复杂系统先进控制与智能自动化湖北省重点实验室,湖北武汉430074 [3]中南林业科技大学计算机与信息工程学院,湖南长沙410004

出　　处：《控制理论与应用》2023年第2期322-330,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(61973284)资助。

摘　　要：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.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.

关 键 词：半Markov切换系统 随机系统 时滞系统 输入–状态稳定性 Lyapunov-Razumikhin函数 不定多重Lyapu-nov函数 时变驻留时间条件 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]