Delay-dependent robust stability analysis for time-delay T-S fuzzy systems with nonlinear local models

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.