Event-triggered Sliding Mode Control for T-S Fuzzy Systems via Two-side Looped Functionals

To address the issues of external disturbances, parametric uncertainties, and communication resource waste in nonlinear systems, we propose an event-triggered sliding mode control (ETSMC) method for Takagi-Sugeno (T-S) fuzzy systems based on two-side looped functionals. Taking a permanent magnet synchronous motor (PMSM) as the control object, a T-S fuzzy model is first established to transform the state-space equation of the nonlinear system into low-order subsystems. A linear sliding surface and an event-triggered scheme are designed for the subsystem, and two-side looped functionals are introduced for stability analysis. Specifically, the two-side looped functionals can completely include all data information by dividing the interval between two adjacent sampling times, which can effectively reduce the constraint on the positive definiteness of the Lyapunov functional and thus significantly lower the conservatism of the stability criteria, ultimately deriving sufficient conditions to ensure stability. Furthermore, the controller gain is obtained based on the stability conditions, and the ETSMC is designed with reachability analysis of the system. The ultimate control objective is to achieve robust stabilization of the PMSM under external disturbances and parametric uncertainties, while reducing the consumption of communication resources. Simulation results verify that the proposed method can stabilize the PMSM rapidly and effectively save communication resources.