New sufficient conditions for delay-dependent robust H∞ control of uncertain nonlinear system based on fuzzy hyperbolic model with time-varying delays

The robust H
∞
control problem was considered for a class of fuzzy hyperbolic model with time-varying delays (DFHM) systems with parametric uncertainties and multiple delays. First, DFHM modeling method was presented for time-delay nonlinear systems. Then, by using Lyapunov-Krasovskii approaches, delay-dependent sufficient condition for the existence of a kind of state feedback controller was proposed, which was expressed as linear matrix inequalities (LMIs). The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H
∞
performance level for all admissible uncertainties and time-delay. Finally, a simulation example was provided to illustrate the effectiveness of the proposed approach.