New sufficient conditions for robust H∞ fuzzy hyperbolic tangent control of uncertain nonlinear systems with time-varying delay

This paper considers the delay-dependent robust H∞ control problem based on fuzzy hyperbolic model (FHM) for a class of uncertain nonlinear systems with time-varying delay. Firstly, FHM modeling method is presented for uncertain nonlinear systems with time-varying delay. Secondly, the new delay-dependent sufficient condition for the existence of a state feedback fuzzy hyperbolic tangent controller is proposed in terms of linear matrix inequalities (LMIs) by constructing a novel Lyapunov–Krasovskii functional. The robust FHM-based control law can guarantee that the closed-loop system is robustly asymptotically stable with a prescribed H∞ index. As more information of the FHM and the size of time-delay are taken into account, the proposed conditions are new and less conservative. Finally, three illustrative examples are given to show the effectiveness of using FHM-based controllers.