${\cal L}_{\infty}$-Gain Adaptive Fuzzy Fault Accommodation Control Design for Nonlinear Time-Delay Systems

Abstract

In this paper, an adaptive fuzzy fault accommodation (FA) control design with a guaranteed L(∞)-gain performance is developed for a class of nonlinear time-delay systems with persistent bounded disturbances. Using the Lyapunov technique and the Razumikhin-type lemma, the existence condition of the L(∞) -gain adaptive fuzzy FA controllers is provided in terms of linear matrix inequalities (LMIs). In the proposed FA scheme, a fuzzy logic system is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown fault function; a continuous-state feedback control strategy is adopted for the control design to avoid the undesirable chattering phenomenon. The resulting FA controllers can ensure that every response of the closed-loop system is uniformly ultimately bounded with a guaranteed L(∞)-gain performance in the presence of a fault. Moreover, by the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(∞)-gain. Finally, the achieved simulation results on the FA control of a continuous stirred tank reactor (CSTR) show the effectiveness of the proposed design procedure.