时滞不确定随机系统基于参数依赖Lyapunov函数的稳定条件  

Stability of uncertain stochastic systems with time-varying delays based on parameter-dependent Lyapunov functional

作　　者：吴立刚[1] 王常虹[1] 高会军[1] 曾庆双[1] 

机构地区：[1]哈尔滨工业大学空间控制与惯性技术研究中心,黑龙江哈尔滨150001

出　　处：《控制理论与应用》2007年第4期607-612,共6页Control Theory & Applications

基　　金：国家自然科学基金(69874008).

摘　　要：针对一类具有凸多面体参数不确定性的时滞随机系统,研究了其鲁棒稳定性问题.通过引入适当的加权矩阵变量来寻找Leibniz-Newton公式各项之间的关系,从而直接地处理系统中的时滞状态项,避免了常规的应用Leibniz-Newton公式来进行模型变换的间接方法所带来的较大保守性.采用参数依赖Lyapunov函数方法,推导了此类系统鲁棒稳定的时滞相关的充分条件.本文所得条件为线性矩阵不等式形式,便于借助于内点算法进行求解.仿真实例证明了本文所提出的稳定条件具有较低的保守性.The robust stability analysis for a class of linear stochastic systems with polytopic-type uncertainties and time-varying delays is considered in this paper. By introducing some slack matrices, and finding the relation between the terms in the Leibniz-Newton formula, a sufficient delay-dependent condition is proposed for the robust asymptotic stability of such a system by applying the parameter-dependent Lyapunov functional approach. In contrast to the traditional method of using model transformation to derive the delay-dependent condition, this new stability condition is less conservative. The resultant stability condition is in the form of linear matrix inequalities （LMIs）, which can be solved via efficient interiorpoint algorithms. A numerical example is also presented to illustrate the less conservative properly of the proposed stability condition.

关 键 词：参数依赖LYAPUNOV函数 时滞相关:随机系统 凸多面体不确定性 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]