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

The author considers 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. It is assumed 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. The author presents a problem formulation and then provides a solution based on it. Not only does he address the existence question but he also gives representations of all controllers from the class that meet the robustness requirements. It is pointed out that the present work represents a serious attempt to take recent Kharitonov-like analysis results and turn them into design tools. The results obtained are sufficient conditions and they are developed using only vertex information from the plant family