Optimal control for Markovian jump systems with colored process noise

This paper investigates optimal controller design for Markovian jump systems with colored process noise. Since the colored process noise can be obtained by white noise through shaping filter, we get new equivalent equations of the concerned systems by using expansion vector method. Based on this, the optimal estimator in mean squared sense is deduced by adopting Kalman filter. According to the separation principle, the feedback controller only depends on the state estimation variables. With the desired controller for such Markovian jump systems, the quadratic control performance of such systems can be minimized. A numerical simulation illustrates the validity of this method.