Positive Realness And Coprime Factor Uncertainty Conditions For Reduction Of Robust Stabilization Problems To Classical H /spl infin/ Problems

摘要

In this paper, we consider the problem of robustly stabilizing a family of linear time-invariant systems with a linear time-invariant controller. We 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/spl infin/ problem. Subsequently, under the imposition of certain positive realness conditions, we show that the robust stabilizability is equivalent to making a certain weighted H/spl infin/ norm less than unity. We also provide a motivating example for a set of similar results involving a coprime factor style description to the uncertainty.