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

This paper deals with the control problem of singularly perturbed systems when the singular perturbation parameter, ε, 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 "regular" 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 methods" 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 ε, 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