Controle Fuzzy T–S Tipo-2 intervalar por modos deslizantes adaptativo acionado por eventos e com garantia de passividade robusta para sistemas com atraso de tempo

Abstract

This thesis addresses the design of event-triggered adaptive sliding mode control for interval type 2 Takagi–Sugeno (T–S) fuzzy nonlinear systems with time-varying delay, subject to matched perturbations with unknown upper bound and unmatched perturbations, with distinct input matrices among the local linear subsystems. Two control methods are proposed, denoted control method 1 and control method 2, which share the same practical stabilization and robust passivity framework while differing in the adaptive law governing the switching gain. In both methods, practical stabilization and robust passivity within the practical sliding mode region are obtained from the robust passivity inequality, with the storage function defined by a fuzzy Lyapunov Krasovskii functional, from which conditions in the form of delay-dependent linear matrix inequalities are derived, dependent on the maximum delay, the upper bounds on the rates of variation of the delay and of the membership degrees, and the robust passivity coefficient. The feasibility of these conditions determines the sliding variable matrix and provides the decision variables required to derive the practical stabilization conditions, whose practical stability region radius, for both methods, is determined independently of the estimate of the upper bound of the matched perturbation, as is the upper bound of the practical sliding mode region. Control method 1 employs an adaptive law based on monotonic growth, which dispenses with knowledge of this bound and forces the gain to converge once the practical sliding mode region is reached. Control method 2 employs an adaptive law based on a barrier function, which relaxes the dominance of the gain over the matched and unmatched perturbations through a relaxation region, allowing the gain to both increase and decrease and yielding a less aggressive control action than the monotonic strategy. For both methods, the positive invariance of the practical sliding mode region is established under the simultaneous presence of time-varying delay, matched and unmatched perturbations, and event-triggered control, with reaching instants independent of the estimate of the upper bound of the matched perturbation. The event-triggering mechanism is formulated with an analytical guarantee of the absence of Zeno behavior, and certification of the maximum admissible delay is carried out via bisection decoupled from the control design. An upper bound for the triggering threshold is further derived, for each method, as a function of the robust passivity coefficient, establishing an energy-based link between the triggering mechanism and the closed-loop dissipativity, while this same coefficient bounds the impact of the unmatched perturbation on the output. The results are validated through computational simulations that demonstrate the effectiveness and comparative advantages of the proposed methods over existing approaches in the literature.