Finite-time control for discrete-time Markovian jump systems with deterministic switching and time-delay
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In this paper, the finite-time control problem is investigated for a class of discrete-time Markovian jump systems (MJLSs) with deterministic switching and time-delay. The considered systems are subject to a piecewise-constant transition probability (TP) matrix, which leads to both the deterministic switches and stochastic jumps. First, the stochastic finite-time boundedness (SFTB) and l 2 gain analysis for the systems are studied by employing the average dwell time (ADT) approach. Note that a finite-time weighted l 2 gain is obtained to measure the disturbance attenuation level. Then, the mode-dependent and variation-dependent controller is designed such that the resulting closed-loop systems are stochastically finite-time bounded and have a guaranteed disturbance attenuation level. Finally, a numerical example is given to verify the potential of the developed results.
KeywordsAverage dwell time finite-time boundedness finite-time weighted l2 gain switching dynamics Markovian jump linear system
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