%0 Journal Article
%T 具有输入时滞的离散时间随机系统Lyapunov镇定性条件<br>Lyapunov-type stabilizating conditions of discrete-time stochastic systems with input delay
%A 谭成
%A 张焕水&lt
%A br&gt
%A TAN Cheng
%A ZHANG Huan-shui
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.507
%X 摘要： 主要研究了具有输入时滞和乘性噪声的离散时间随机系统渐近均方镇定性问题。首先,基于Lyapunov不等式,给出易于验证的系统渐近均方镇定性的充分条件。其次,基于耦合Lyapunov方程,得到系统渐近均方镇定性的必要性条件。值得注意的是,当所研究系统退化为无时滞随机系统或确定性时滞系统,系统的渐近均方镇定性等价于耦合Lyapunov方程解的存在唯一性。<br>Abstract: This paper mainly studies the asymptotical mean square stabilization problem for discrete-time stochastic system with single input delay and multiplicative noises. First, expressed by Lyapunov-type inequalities, some sufficient and easily verified stabilizing conditions in mean square sense are developed. Second, based on the derived coupled Lyapunov-type equations(CLEs), a necessary condition is developed. It is remarkable that when the considered stochastic system with input delay degrades into the stochastic system without input delay or the deterministic time-delay system, the reduced system is asymptotical mean square stabilizable if and only if the given CLEs have unique solutions
%K 渐近均方镇定性
%K 输入时滞
%K 随机系统
%K 耦合Lyapunov方程
%K &lt
%K br&gt
%K stochastic system
%K coupled Lyapunov-type equation
%K input delay
%K stabilization
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.507