An interpolation method for the control of έ-varying singularly perturbed systems

Abstract

This paper deals with the control problem of singularly perturbed systems when the singular perturbation parameter, /spl epsi/, varies smoothly between a very small and a large value. This variation makes the dynamics of system to evolve between a singularly perturbed behavior and a behavior, or between two different singularly perturbed behaviors, ie., the fast dynamics becoming slow and the slow ones becoming fast. It is clear that in such situations, neither singular perturbations approach, nor regular alone are efficient globally. To deal with this problem, we propose a control law which essentially combines techniques of singular perturbations and stable scheduling-interpolation methods to build a globally stable and efficient controllers. Based on the variations of /spl epsi/, several local stable controllers are first designed using singular perturbations approaches or regular methods, and then they are interpolated in a way that guarantees global stability.