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Finite-time H∞ Control of Stochastic Singular Systems with Partly Known Transition Rates via an Optimization Algorithm

Zhengtian Wu*, Lijian Yang, Baoping Jiang, and Yonggui Kao
International Journal of Control, Automation, and Systems, vol. 17, no. 6, pp.1462-1472, 2019

Abstract : This paper is concerned with the problem of finite-time H∞ control for stochastic singular systems with partly known transition rates (TRs). The transition of system parameters follows a finite-state Markov process. Firstly, based on stochastic functional method and linear matrix inequalities (LMIs) technique, sufficient conditions are proposed to ensure finite-time stochastic boundedness (FTSB) and finite-time H∞ stochastic boundedness (FTH∞SB) of considered stochastic singular system. Secondly,by designing a state feedback controller,strictLMI conditions are obtained to guarantee the closed-loop system with partly known TRs to be FTSB and FTH∞SB. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methods.

Keyword : "Finite-time stochastic stability, H∞ control, singular systems, stochastic systems. "

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