Delay-Dependent Stability of a Class of Nonlinear Systems with Time Delays Based on Fuzzy Hyperbolic Model

Abstract

This paper concerns a problem of delay-dependent stability of a class of nonlinear continuous-time systems with time delays, based on the fuzzy hyperbolic model (FHM). FHM is a universal approximator, and can be used to establish the model for unknown complex systems. Moreover, the main advantage of using FHM over T-S fuzzy model is that no premise structure identification is need and no completeness design of premise variables space is need. Also an FHM is a kind of valid global description and nonlinear model inherently. The proposed method is addressed by solving a set of linear matrix inequalities (LMIs). A general Lyapunov-Krasovskii functional are used and some additional free-weighting matrices, which bring much flexibility in solving LMIs, are introduced during the proof. The results then have easily been extended to a system with either polytopic-type or norm-bounded uncertainties. A simulation example is given to validate the proposed results.