具有输入时滞的离散时间随机系统Lyapunov镇定性条件

doi:10.6040/j.issn.1671-9352.0.2015.507

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (5): 114-120.doi: 10.6040/j.issn.1671-9352.0.2015.507

具有输入时滞的离散时间随机系统Lyapunov镇定性条件

谭成,张焕水^*

山东大学控制科学与工程学院, 山东济南 250061

收稿日期:2015-10-30 出版日期:2016-05-20 发布日期:2016-05-16
通讯作者: 张焕水(1963— ), 男,博士,教授,研究方向为最优鲁棒控制与估计,传感器网络系统,时滞系统,随机系统. ;E-mail:hszhang@sdu.edu.cn E-mail:tancheng1987love@163.com
作者简介:谭成(1987— ),男,博士研究生,研究方向为时滞系统,随机系统,网络控制系统,镇定性. E-mail:tancheng1987love@163.com
基金资助:
山东省泰山学者建设工程项目;国家自然科学基金资助项目(61120106011,61203029)

Lyapunov-type stabilizating conditions of discrete-time stochastic systems with input delay

TAN Cheng, ZHANG Huan-shui^*

School of Control Science and Engineering, Jinan 250061, Shandong, China

Received:2015-10-30 Online:2016-05-20 Published:2016-05-16

摘要/Abstract

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。

关键词: 渐近均方镇定性, 输入时滞, 随机系统, 耦合Lyapunov方程

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.

Key words: stochastic system, coupled Lyapunov-type equation, input delay, stabilization

中图分类号:

TP13

谭成,张焕水. 具有输入时滞的离散时间随机系统Lyapunov镇定性条件[J]. 山东大学学报（理学版）, 2016, 51(5): 114-120.

TAN Cheng, ZHANG Huan-shui. Lyapunov-type stabilizating conditions of discrete-time stochastic systems with input delay[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 114-120.

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具有输入时滞的离散时间随机系统Lyapunov镇定性条件

Lyapunov-type stabilizating conditions of discrete-time stochastic systems with input delay

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