Representations of controllers that achieve robust performance for systems with real parameter uncertainty

Consider a family of single input single output plants described by transfer functions that involve real parameter uncertainty. Parameter values are known to lie in a hypercube. Assume that a class of available controllers has been prescribed, along with a bound for the sensitivity transfer function to ensure tracking. It is of interest to determine whether a controller from the given class exists that guarantees robust stability and robust asymptotic tracking. In this paper we present a problem formulation and then provide a solution based on it. Not only do we address the existence question but also give representation of controllers from the class that meet the robustness requirements.