Finite-Time Composite Disturbance Rejection Control for Discrete-Time Markovian Jump Systems

In this article, the compositedisturbance rejection control approach is established for discrete-time Markovian jump systems with unknown external disturbance. With the transformed system in the regular form, a new mode-dependent disturbance observer is proposed to estimate the unknown disturbance in the absence of the exosystem of the disturbance. Then, the chattering-free controller is designed in the backstepping framework, and the disturbance estimate is incorporated to achieve active disturbance rejection. It can be seen that with the proposed control approach, both the states of the disturbance estimation error systems and the closed-loop systems are finite-time bounded in mean square. Finally, two numerical examples are presented to show the effectiveness of the proposed control approaches.