Fuzzy control of ε-varying singularly perturbed systems

The paper deals with the problem of singularly perturbed systems when the parameter epsilon, representing the ratio speed between the fast and slow dynamics, is time-varying. We will show that using an adequate fuzzy partition of epsilon, we can combine techniques of fuzzy control and singular perturbations to control the system. The parameter epsilon, may be only partially known (known only on some particular "representative" points). The lack of information is recovered using a method of fuzzy approximation, that provides in the game time the partition required to build the control law. The paper ends with an illustrative example.