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

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 2D system is asymptotically mean-square stable (AMSS) with an H-infinity 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.

Automated summary

This article investigates the use of asynchronous sliding-mode control (SMC) for 2-D discrete-time Markov jump systems. A hidden Markov model is employed to describe the asynchronization between the system modes and controller. A new 2-D sliding surface is constructed and an asynchronous SMC law is designed. The reachability of system dynamics to the sliding surface is investigated using Lyapunov function and linear matrix inequality approaches, and conditions for asymptotic mean-square stability and disturbance attenuation performance are established. An algorithm is provided to derive the asynchronous 2D-SMC law, and the validity and effectiveness of the new SMC law design algorithm are verified through an example.