Controllers design for a class of Markov jump linear discrete systems

In this paper, the necessary and sufficient conditions on the existence of the stabilizing controllers of Markov jump linear discrete systems are established in terms of matrix inequality, and the controller design ensuring the stochastic stability of systems is also proposed by using the cone complementarity linearization method. The controller proposed can ensure the stochastic stability of systems, but not all eigenvalues for every discrete subsystem are in unit circle. The proposed controller design ensuring the stochastic stability of systems reduces conservative degree. The simulation results illustrate the effectiveness of the proposed controller design.