Sliding Mode Control of Markovian Jump Fuzzy Systems: A Dynamic Event-Triggered Method

In this article, the sliding mode control (SMC) problem is addressed for a class of Markovian jump systems via the T–S fuzzy model. First, in order to reduce the frequency of state transmission for alleviating congestion phenomenon in the bandwidth-limited communication network, a dynamic event-triggered (DET) strategy is introduced into the sensor-to-controller channel, in which an additional internal dynamical variable is employed to adjust the event-triggered condition adaptively. A fundamental issue resulting from the event-triggered strategy is that the controller cannot obtain the information about system mode during the triggering interval. Aiming at the phenomenon, this work utilizes a mode detector to estimate the unavailable system mode. Then, this article proposes a detected-mode-dependent event-triggered sliding mode controller whose membership grades are determined only via the transmitted state at the triggering instant. By constructing a relation on the membership functions (MFs) between the fuzzy model and the controllers for MF-dependent analysis, the conditions on the reachability and stability conditions are relaxed. Furthermore, an optimization algorithm is provided for the minimum control power via a high-dimensional grid searching for the coefficients of the internal dynamic variables, which, together with the designed detected-mode-dependent sliding mode controller, constitutes the novel SMC scheme under the DET strategy. Finally, the simulation results via the single-link arm system are provided to illustrate the efficiency of the proposed method.