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

dThis paper deals with the problem of control of singularly perturbed systems when the singular perturbation parameter, e:, 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, i.e. the fast dynamics becoming slow and the slow ones becoming fast. It is clear that in such situations, nor singular perturbations approach, neither "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 epsilon, first several local stable controllers are designed using singular perturbations approaches or "regular methods" and, then they are interpolated in a way that guaranties global stability.