Stabilization of nonlinear systems with piecewise bilinear models derived from fuzzy if-then rules with singletons

This paper deals with the modeling and stabilization of nonlinear control systems approximated by fuzzy if-then rules with singleton consequents. The approximated model is found to be piecewise bilinear. First, an optimal method of piecewise bilinear approximation of nonlinear functions is shown. Then, the method of input-output feedback linearization is applied to stabilize piecewise bilinear control systems. An illustrative example is given to show the validity of the proposed methods.