Robust stability and stabilisation conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach

This paper deals with the robust stability and robust stabilization problems for nonlinear systems with time-delay and norm bounded uncertainties which can be represented by Takagi-Sugeno (T-S) uncertain fuzzy model with time-delay. Based on fuzzy weighting-dependent Lyapunov-Krasovski functional approach and the free weighting matrix method, stability sufficient conditions are proposed and then extended to stabilization problem via the concept of the so-called parallel distributed compensation (PDC). To reduce the conservatism, the new stability conditions obtained by introduction the slack variables are derived in terms of Linear Matrix Inequalities (LMIs). It is shown that the obtained conditions provide less conservative results than some existing ones. Finally, to show the effectiveness of the proposed method in term the conservatism reduction, the simulation examples are given.