Robust preview control of uncertain discrete-time T-S fuzzy Markovian jump systems subject to time-varying delays via sliding mode approach

Abstract

For a class of uncertain discrete-time T-S fuzzy Markovian jump system (MJS) subject to time-varying delays, the problem of the sliding mode preview control (SMPC) is studied in this work. Due to the existence of the Markovian chain and uncertain time-varying coefficients, the traditional difference method is no longer applicable. In this paper, an approach combining the robust control technique is adopted to avoid the difference. An augmented error system (AES) is built to deal with the preview information, in which an integrator is introduced to mitigate the static error. The SMPC problem is thereby transformed into a stabilization problem. A mode-independent sliding surface is designed for the AES. Then, a sliding mode preview controller based on the sliding surface is synthesized by which the stochastic stability of the quasi-sliding motion (QSM), as well as the reachability of a sliding region around the specified sliding surface, can be guaranteed simultaneously. Finally, we give two examples to show that the original system output can track the reference signal well by the proposed sliding mode preview controller.