Output Feedback Control of Piecewise Homogeneous Semi-Markov Jump Systems

This brief addresses the output feedback control problem of semi-Markov jump systems with unfixed transition probabilities. A high level homogeneous Markov chain is employed to describe the variation of transition probabilities of the piecewise embedded homogeneous Markov chain. After studying the influence of transition probabilities on the system dynamics, and relaxing the requirement of Lyapunov function at jump instants, improved stability conditions are proposed which are tightly associated with the time-varying transition probabilities. Finally, a numerical example and an RLC circuit are presented to show the usefulness of incorporating the information of transition probabilities and to illustrate the effectiveness of the designed controllers.