Robust finite-time Hα control for uncertain discrete-time singular systems with Markovian jumps

This study is concerned with the finite-time H_∞ control problem for uncertain discrete-time Markovian jump singular systems with time-varying norm-bounded disturbance. Firstly, the concepts of singular finite-time stability, singular finite-time boundedness and singular H_∞ finite-time stabilisation are given. Then, sufficient conditions of singular finite-time boundedness and singular H_∞ finite-time stability are derived for the class of discrete-time Markovian jump singular systems. The main contribution of the study is to propose a numerical efficient and reliable controller design process for state feedback finite-time H_∞ control of discrete-time Markovian jump singular systems. By applying the descriptor system technique presented by Fridman and Shaked, sufficient criteria are presented for the solvability of the problems, which can be reduced to feasibility problems in terms of linear matrix inequalities. Finally, numerical examples are included to illustrate the validity of the presented results.