Two-Dimensional Asynchronous Sliding-Mode Control of Markov Jump Roesser Systems

• Published in: IEEE transactions on cybernetics 2022-04, Vol.52 (4), p.2543-2552
• Main Authors: Tao, Yue-Yue, Wu, Zheng-Guang, Guo, Yingxin
• Format: Article
• Language: English
• Subjects: 2-D systems; Algorithms; Attenuation; Boundary conditions; Control systems; Controllers; Discrete time systems; Hidden Markov model; Hidden Markov models; Liapunov functions; Linear matrix inequalities; Markov chains; Markov jump systems; Markov processes; Mathematical analysis; Mathematical model; Sliding mode control; sliding-mode control (SMC); System dynamics
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2020.3006329

In this article, asynchronous sliding-mode control (SMC) is investigated for 2-D discrete-time Markov jump systems. As the system modes are not always accessible to the controller, the hidden Markov model is employed to describe the asynchronization between the system modes and controller. A new 2-D sliding surface is constructed and the corresponding asynchronous SMC law is designed under the framework of the hidden Markov model. By Lyapunov function and linear matrix inequality (LMI) approaches, the reachability of system dynamics to the predefined sliding surface is investigated, and sufficient conditions are established to guarantee that the underlying 2-D system is asymptotically mean-square stable (AMSS) with an H_{\infty } disturbance attenuation performance. Then, an algorithm is provided to derive the asynchronous 2D-SMC law. Finally, an example is given to verify the validity and effectiveness of the new SMC law design algorithm.