A new approach to robust finite-time H_∞ control of continuous-time Markov jump systems

This paper studies the robust finite-time H_∞ state feedback control problem of continuous-time Markov jump systems (MJSs) subject to norm bounded uncertainties. Transition probabilities are allowed to be known, uncertain with known bounds or unknown. Based on the continuous transition probability property and the developed slack variable technique, Lyapunov variables are separated from unknown transition probabilities and system matrices. With these separations, a relaxed method for robust finite-time H_∞ controller design is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of and the benefit from the proposed method.