This report documents research in the areas of stability and performance robustness. Stability robustness in the presence of structured and unstructured uncertainty is discussed relative to nonminimum phase systems. Simultaneous stabilization under unstructured uncertainties and nonconservative stability robustness bounds are addressed. Performance robustness is discussed using the D-Stability formulation. Keywords: Control, Structured uncertainty, Stabilization systems, Simultaneous equations, Phase locked systems. (CP).

This volume collects most of the papers presented at the International Workshop on Robustness in Identification and Control, held in Torino (Italy) in 1988. The main focal point of the workshop was Unknown But Bounded uncertainty and associated robustness issues in identification and control. Recent years have seen a growing interest in studying models which include un known but bounded uncertainty. The motivation for dealing with such models is derived from robustness considerations. In many applications, some performance specification must be met for all admissible variations of the uncertain parameters. A second motivation for models with this type of uncertainty stems from the fact that the statistical description of uncertain variables may not be well known or even not suitable. For example, in some cases, only a small number of measurements is available and the resulting errors are due to analog-digital conversion, modelling ap proximation or round-off, so that a statistical description may actually be unreliable. The interest in unknown but bounded setting is certainly not new. In fact, en gineering practice demands for appropriate algorithms in dealing with finite sample properties, finite parameter variations, tolerance analysis, etc. Despite the natural need for such methods, the lack of sufficiently well assessed theoretical results and algorithms prevented a systematic use of these procedures until recent years. How ever, in the last few years, important advances have been made both in estimation theory and in stability analysis.

This book presents a number of techniques for robustness analysis of uncertain systems. In it, convex relaxations for several robustness problems are derived by exploiting and providing new results on the theory of homogenous polynomial forms.