具有凸多面体不确定性的混杂随机微分方程的镇定分析

摘要

This paper deals with the problem of stabilizing a stochastic differential equation with Markovian switching and polytopic uncertainties.State-feedback controllers are designed based on discrete-time observations of the system.The controllers will be put into both drift and diffusion terms so that the controlled system will be exponentially stable in mean-square.The time lag τ is led to the system.The criteria to determine controllers and time lags are obtained by applying Lyapunov functions to analyze the system.Then the feedback controllers are designed based on the theoretical basis of the criteria above.The linear matrix inequality is used to obtain the satisfied conditions for coefficient matrix of the controller,namely the stabilizability criteria of the equation.The numerical example verifies the feasibility of the method.%研究了带有马尔科夫切换的具有凸多面体不确定性的随机微分方程的稳定化问题.基于离散的系统观测状态设计了反馈控制器,将控制项同时添加在漂移项和扩散项中,使得控制系统均方指数稳定.在控制系统中引入时滞量τ,利用Lyapunov函数方法对控制系统进行分析,得到了使控制系统稳定的反馈控制器满足的条件以及时滞量的确定准则,并以此为理论基础设计控制器,应用线性矩阵不等式方法得到了控制项系数矩阵满足的条件,即微分方程的可镇定判据.具体的数值算例验证了该方法的可行性.