Event-triggered observer-based sliding mode control for T-S fuzzy systems via improved relaxed-based integral inequality

Abstract

This paper performs the observer-based exponential stabilization criterion for event-triggered fuzzy systems using observer-based sliding mode fuzzy control subject to limited communication resources and unmeasurable premise variables. The nonlinear control system is modeled through a fuzzy model by considering the observer-based sliding mode control with event triggered mechanism. A discrete-time event-triggered scheme has been proposed to determine the unmeasurable states of the proposed system. To deal with the integral factors occurring in the derivate of the Lyapunov–Krasovskii functional (LKF), a new relaxed-based integral inequality has been introduced as a combination of Wirtinger-based inequality and reciprocally convex lemma together with the proposed Lemma. By employing this new integral inequality and by the Lyapunov stability theory, the exponential stability conditions with the prescribed observer and controller gain matrices are attained for ensuring the exponential stability of the T-S fuzzy system. Finally, the proposed theoretical results are applied to the truck-trailer model to validate the effectiveness of the proposed approach.