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Reachable Set Estimation for Itô Stochastic Semi-Markovian Jump Systems Against Multiple Time Delays

Shaoxin Sun, Xin Dai*, Ruipeng Xi, Yuliang Cai, Xiangpeng Xie, and Chunhua Zhang
International Journal of Control, Automation, and Systems, vol. 20, no. 9, pp.2857-2867, 2022

Abstract : The work deals with these issues of stochastic finite-time boundedness (SFTB), reachable set estimation with input-output finite-time mean square stabilization (IO-FTMSS) for multiple state delayed semi-Markovian jump models subject to uncertainties, stochastic process as well as input constraint. There are few attempts to perform related studies. Firstly, a nonlinear passive control mechanism is designed. Then, a closed-loop model could be acquired. Through stochastic Lyapunov function, these problems of SFTB, reachable set estimation with IO-FTMSS could be solved. In addition, these stability conditions are provided in the framework of linear matrix inequalities. These controller gain matrices, meanwhile, can be derived. At last, this availability of this described strategy can be proved through one simulation.

Keyword : Fault-tolerant controller, Itô stochastic semi-Markovian jump systems, linear matrix inequalities (LMIs), reachable set estimation, time-varying delays.

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