Design of adaptive fuzzy integral sliding mode control for uncertain nonlinear systems with state and input delays

This paper addresses the problem of adaptive fuzzy integral sliding mode control (AFISMC) for uncertain nonlinear systems with state and input delays. First, we employ a state-transformation to map the nonlinear system into an input-delay free system. Then, an adaptive fuzzy technique is applied to estimate the bound of the lumped perturbation. Finally, based on Lyapunov stability theorem, a controller is proposed to guarantee the stability of the overall system. An illustrative example is provided to demonstrate the usefulness of the proposed controller.