Real-Time Reachable Set Control for Singular Markov Jump Networked Cascade Systems

Liang Zhang, Guangdeng Zong, Xudong Zhao, Ning Zhao

Abstract: This study is concerned with the problem of real-time reachable set (RS) control for a class of singular Markov jump (SMJ) networked cascade systems with time-delay, disturbance and non-zero initial conditions. Aiming at the shortcoming that the output of the controlled object is non-zero disturbance in single loop feedback control, an SMJ networked cascade control system model is proposed. By utilizing the Lyapunov stability theory, the linear matrix inequality technique and the free-weighting matrix method, the sufficient stability conditions and the real-time RS boundary for the closed-loop stochastic systems are obtained. Then, the gains of the cascade controller are represented by a reasonable matrix decoupling method. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method.