Sliding mode control of nonlinear uncertain system based on Takagi-Sugeno fuzzy model

This paper proposes an approach to design sliding mode control for a class of uncertain nonlinear systems, where the uncertainty is a norm bounded type. Firstly, we choose the sliding surface which gives a good behaviour during sliding mode. It is formulated as an assignment of the poles of uncertain nonlinear system in a convex optimization area. Secondly, we design a nonlinear control law leading the state trajectory on the sliding surface in a finite time. A numerical application of inverted pendulum is given to validate the theoretical results of our approach.