Graphical analysis of robust stability for systems with parametric uncertainty: an overview

Abstract

Systems with parametric uncertainty play an important role in both the theory and practical applications of robust control. They are described by the mathematical model containing parameters that are not precisely known, but the values thereof lie within given intervals. This type of uncertainty can arise during the control of real processes, eg, as a consequence of modelling effort, imprecise measuring or the influence of certain external conditions. The number of robust stability analysis techniques has been developed during the previous years of research interest. However, many of them are highly specialized only for specific types of uncertainty structure. This paper offers an overview of illustrative examples aimed at usage of a universal graphical approach to robust stability analysis for systems with parametric uncertainty. The investigation method is based mainly on the combination of the value set concept and the zero exclusion condition, which is greatly advantageous especially for more complicated problems.