Decomposition of near-optimum regulators with nonstandard multiparameter singular perturbations

Near-optimal control of multiparameter nonstandard singularly perturbed systems is studied using the descriptor variable approach. The slow models of the systems considered may exhibit impulses. Under stabilizable and detectable assumptions on the slow models and a block-D stabilizable assumption on the fast or boundary layer systems, the near-optimum regulators are completely decomposed. It is shown that the near-optimal control is a cascade connection of slow and fast subregulators that are independent of the perturbed parameter vector ∈, and that the slow and the fast subregulators can be designed separately. The frequency responses of the near-optimum systems are derived. Several numerical design examples are presented