Hidden-Markov-Model-Based Asynchronous $H_{\\infty }$ Tracking Control of Fuzzy Markov Jump Systems

Abstract

This article is concerned with the problem of imperfect premise matching asynchronous <inline-formula><tex-math notation= LaTeX >$H_{\\infty }$</tex-math></inline-formula> output tracking control for Takagi–Sugeno fuzzy Markov jump systems. A hidden Markov model is established due to the fact that the modes information of the system may not be accurately transmitted to the controller, which is used to depict the asynchronous phenomenon between the system modes and controller modes. The packet loss in the communication process is described by a stochastic variable subject to Bernoulli distribution. Then, based on a novel Lyapunov function, the mode-dependent and fuzzy-basis-dependent stability criteria are derived and the asynchronous control scheme is developed subject to an <inline-formula><tex-math notation= LaTeX >$H_{\\infty }$</tex-math></inline-formula> tracking performance. Finally, two examples are provided to demonstrate the effectiveness of the proposed approach.