时变时滞离散马尔科夫跳变系统的随机镇定设计OA

This paper studies the problem of designing a state feedback controller for the time-varying de-layed discrete Markov jump system with two independent Markov chains and partially unknown transition probabilities.Firstly,in order to avoid the occurrence of time-varying delayed dependent non-convex poly-nomials,the augmented state correlation vector and the zero equation of the extended free weight matrix are introduced to improve the efficiency of stability analysis and reduce the conservativeness of stability criteria.Secondly,concerning the properties of the partially unknown transition probability matrix,a less conservative sufficient condition for the stochastic stability of the considered system is established by con-structing improved Lyapunov-Krasovskii functionals and by utilizing the auxiliary-function-based sum ine-quality as well as the reciprocally convex combination inequality.In addition,the state feedback controller gains of the considered system are designed by linear matrix inequalities,Finsler lemma and matrix substi-tution method.Finally,the feasibility and effectiveness of the proposed control design scheme are verified through a comparative numerical simulation example.