Two-Dimensional Asynchronous Sliding-Mode Control of Markov Jump Roesser Systems
Yue-Yue Tao, Zheng‐Guang Wu, Yingxin Guo
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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.