离散奇异马尔科夫跳变系统的广义二次随机稳定性和可镇定问题研究

Study of Problems of Generalized Quadratic Stochastical Stability and Stabilization for Uncertain Discrete-time Singular Markovian Jump System

研究了离散奇异马尔科夫跳变系统的鲁棒随机稳定性和鲁棒随机可镇定问题.首先给出了以严格线性矩阵不等式表达的离散奇异马尔科夫跳变系统随机容许性充要条件,在此基础上引入广义二次随机稳定性和广义二次随机可镇定的概念,然后分别导出了以严格线性矩阵不等式表达的不确定离散奇异系统广义二次随机稳定性和广义二次随机可镇定充要条件,同时给出了状态反馈控制器的显式表达式.

The problems of robust stability and stabilization for uncertain discrete-time singular Markovian jump system are studied.Firstly,a necessary and suffcient condition for a discrete-time singular Markovian jump system（MJL） to be stochastically admissible is proposed in terms of a strict linear matrix inequality（LMI）.On the basis of this,the concepts of generalized quadratic stochastical stability and generalized quadratic stochastical stabilization for uncertain discrete-time MJL systems are introduced.Then necessary and suffcient conditions for generalized quadratic stochastical stability and generalized quadratic stochastical stabilization are derived in terms of a strict LMI and a set of matrix inequalities,respectively.With these conditions,the problems of stochastically robust stability and stochastically robust stabilization are solved.An explicit expression of a desired state feedback controller is also given.