Robust feedback control of a class of singularly perturbed uncertain dynamical systems

A class of uncertain singularly perturbed control systems described by ordinary differential equations is considered. The uncertainties are characterized deterministically: the singular perturbation is characterized by a real nonnegative system parameter μ. For μ=0, the system order is lower than that for μ>0. Based only on information available on the uncertain reduced-order (μ=0), controllers are proposed which assure that the behavior of the feedback-controlled reduced-order system is close to that of global uniform asymptotic stability about zero. Subject to the same controllers, the full-order system (μ>0) has the same qualitative behavior, provided μ<μ*, where μ*>0 can be computed from the available information