Input–output finite-time stabilisation of Markovian jump systems with incomplete transition rates: a sliding mode method

ABSTRACT In this paper, the input–output finite-time stabilisation (IO-FTS) problem for a class of Markovian jump systems is investigated, in which some elements in the transition rate matrix are partially known and an explicit output constraint condition is required, i.e. the system output (weighted) norm does not exceed an assigned threshold β. An extended definition of IO-FTS is firstly given to reduce the conservativeness arising from zero initial condition . A parameter-dependent sliding mode control strategy is proposed to eliminate the effect of partially known transition rates such that state trajectories are driven to the specified sliding surface during a given finite (possibly short) time interval. Besides, the sufficient conditions are derived to ensure the IO-FTS of the closed-loop systems over the finite-time interval including the reaching phase and the sliding motion phase. Finally, a simulation example illustrates the validity of the proposed method.

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