Relaxed robust stabilization of nonlinear systems with parametric uncertainties

This paper addresses stability analysis and robust stabilization for nonlinear systems in the presence of parametric uncertainties. The Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties is used as the model for the uncertain nonlinear system. Both continuous-time and discrete-time cases of the T-S fuzzy system are considered. In the two cases, sufficient conditions are proposed for robust stabilization in the sense of Lyapunov asymptotic stability, which are represented in the form of linear matrix inequalities. Finally, the T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a simulation platform. The validity and applicability of the proposed approach are successfully demonstrated by means of the numerical simulation for the continuous-time nonlinear system.