Design of robust fuzzy Sliding-Mode control for a class of the Takagi-Sugeno uncertain fuzzy systems using scalar Sign function

This article presents a fuzzy sliding-mode control scheme for a class of Takagi-Sugeno (T-S) fuzzy which are subject to norm-bounded uncertainties in each subsystem. The proposed stabilization method can be adopted to explore T-S uncertain fuzzy systems (TSUFS) with various local control inputs. Firstly, a new design is proposed to transform TSUFS into sliding-mode dynamic systems.In addition, the proposed stabilization condition for the sliding-mode dynamic system can be formulated in terms of linear matrix inequalities (LMIs) using the Lyapunov functions. Finally, the validity of the proposed design strategy is demonstrated through the simulation of an inverted pendulum on a cart. According to simulation results, the performance indexes of the proposed method can achieve satisfactory results with minimum energy control effort, faster response, and zero steady-state error.