A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities

This paper is concerned with the state feedback control of continuous Markov jump linear systems with incomplete transition probabilities in finite frequency domain. By developing a new technique to handle the coupling among Lyapunov variable, system matrix and controller parameter, new sufficient conditions for the closed-loop system to be stochastically stable with the required finite frequency performance are established in terms of linear matrix inequalities. Meanwhile, the finite frequency state feedback controller is also obtained by the proposed conditions directly. The validity of the proposed method is demonstrated by a numerical example.