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

中文关键词  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

英文关键词  parameter-dependent Lyapunov functional  delay-dependent  stochastic systems  polytopic-type uncertainties  linear matrix inequalities (LMIs)

中文摘要

      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.

英文摘要

      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.