Variable structure control problems and the theory of singular perturbations

The authors use the classical theory of singularly perturbed systems to design a dynamical feedback controller which allows solution of control problems, involving sliding manifolds, within a prescribed approximation error. The dynamical feedback controller is the solution of a differential equation containing a small parameter ∈>0. The equation is derived from the data of the considered problem. The controller turns out to be an absolutely continuous function and so the chattering phenomenon is practically eliminated. The relationship between the controller and the equivalent control is investigated. The behavior of the controlled response of the system to disturbances is also studied