Delay-Dependent Robust Stability Analysis for Time-Delay T–S Fuzzy Systems with Nonlinear Local Models

Abstract

This paper addresses the robust stability problem for nonlinear systems subjected to model uncertainties and with time-delay and its derivative varying within intervals. The nonlinear time-delay system is described by a new Takagi-Sugeno fuzzy model consisted of local nonlinear time-delay systems. The new fuzzy model has fewer fuzzy rules than conventional T–S fuzzy models with local linear time-delay systems; therefore, can be more easily derived in practical situations. To reduce conservatism concerning both models, a stability analysis which incorporates state-of-the-art stability techniques with an improved piecewise analysis method, amended with novel delay-interval-dependent terms, is proposed. The proposed analysis, based on a novel fuzzy weighting-dependent Lyapunov-Krasovskii functional, considers that the delay-derivative is either upper and lower bounded, bounded above only, or unbounded, i.e., when no restrictions are cast upon the derivative. Numerical examples are provided to enlighten the importance and the conservatism reduction of the proposed method which outperforms state-of-the-art criteria in time-delay systems literature.