Covariance averaging in the analysis of uncertain systems

Abstract-The effects of parametric uncertainty in stable state space systems are analyzed by averaging the state covariance over the statistics of the uncertain parameters. For natural frequency uncertainty, this computation is related to the Fourier transform of the probability density function of the uncertain parameter. Equipartition and incoher-ence are illustrated for a single mode oscillator. Averaging over a discrete uncertainty model yields the Bourret design equations, while averaging over a Cauchy uncertainty distribution yields the “maximum entropy’ ’ covariance equation of Hyland. I. INTRODUCTTON In recent years, there has been significant progress in analysis and compensator synthesis for systems with unstructured uncer-tainty. However, problems with parametric uncertainty are much less well understood. The goal of this note is to examine the effects of parametric uncertainty in stable state space systems b