A constructive stability condition for a class of multivariable fuzzy controllers

The paper is concerned with control systems with a fuzzy controller feedback. We investigate a class of multivariable SUGENO fuzzy controllers. An explicit formula for the fuzzy controller is restated and a formula for its linearization is given in terms of some parameters of the fuzzy controller, e.g. membership functions and rule base. Based on this, linear stability analysis yields conditions suitable for controller analysis as well as for controller synthesis. The method is demonstrated by the well-known inverted pendulum Example. The eigenvalues of the closed-loop linearization of the pendulum with fuzzy controller are explicitly calculated.