Global stability of fuzzy systems based variable structure control

Global and asymptotic stability of a fuzzy system represented by the Affine Takagi-Sugeno (T-S) model controlled by a fuzzy variable structure controller (VSC) is presented. In this paper, new conditions for the global stability, are developed. A design of a robust fuzzy based Variable Structure Controller is presented to stabilize and improve the response of non-linear unstable systems. Both the fuzzy controller (FC) and the controlled system are represented by the affine T-S fuzzy model. A control strategy is proposed to reduce the chattering problem which is considered the main drawback of the VSC by introducing a boundary layer around the switching surface. A simulation study for an inverted pendulum mounted on a cart is used to demonstrate the design procedure. The results obtained show a robust and stable behaviour when the system is subjected to an impulse and perturbation effect.