Sliding-Mode Control for IT2 Fuzzy Nonlinear Singularly Perturbed Systems and Its Application to Electric Circuits: A Dynamic Event-Triggered Mechanism

Abstract

This work is devoted to an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> sliding-mode control for nonlinear singularly perturbed system under a network control framework. Aiming at describing the nonlinearities with parameter uncertainties in the studied system, the idea of interval type-2 (IT2) fuzzy method is employed in the system modeling. A disturbance observer is developed to acquire the unknown disturbance, and the estimated value is implemented into the controller for neutralizing the influence of the disturbance. To further reduce the occupation of network resources, an event-triggered communication protocol with a dynamic threshold parameter is adopted, where the triggered condition can be adjusted adaptively as the evolution of the system states. Then, an appropriate fuzzy integral sliding motion is constructed based on the constructed system model and disturbance estimation. It is worth noting that the constructed fuzzy controller follows the idea of nonparallel distribution compensation, which improves the designed flexibility. In terms of fuzzy processing, by introducing the membership functions dependent method into the stability analysis, a series of relaxed criteria are established to ensure the global asymptotic stability for the closed-loop systems with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> performance level. Finally, two classical examples of circuit model and inverted pendulum model are extended to IT2 fuzzy idea, showing the rationality of the proposed approach.