Positive realness and coprime factor uncertainty conditions for reduction of robust stabilization problems to classical H∞ problems

Considers the problem of robustly stabilizing a family of linear time-invariant systems with a linear time-invariant controller. The authors work with classes of systems with real uncertain parameters entering affinely into the numerator or denominator of the plant (but not both simultaneously) and seek a "one-shot" solution by reducing the robust stabilization problem to a standard H^∞ problem. Subsequently, under the imposition of certain positive realness conditions, it is shown that the robust stabilizability is equivalent to making a certain weighted H^∞ norm less than unity. The authors also provide a motivating example for a set of similar results involving a coprime factor style description of the uncertainty.