Event-Triggered Sliding Mode Control of Fuzzy Systems via Artificial Time-Delay Estimation

In this article, we show that a fuzzy system of relative degree two can be stabilized by proportion-integration-differentiation (PID) sliding mode control depending on the outputs and their derivatives. The main focus of this article is to formulate a novel event-based fuzzy PID sliding surface under the imperfect premise matching. First, the measured output is adequately sampled for frequently checking a delay-dependent event-triggered condition, which reduces the number of data transmissions and controller updates. Then, an artificial time-delay estimator is used to approximate the output derivative. Based on linear matrix inequalities, a heuristic algorithm is investigated to design an event-triggered sliding mode controller, which reveals how to choose the maximum sampling interval that maintains the estimation accuracy and preserves the stability under fast event triggering. In simulation, the effectiveness of the proposed design method is verified in a cart and pendulum system subject to system uncertainties.