Two approaches to description and robust stability analysis of fractional order uncertain systems

Abstract

The principal goal of this contribution is to present two different approaches to description and robust stability analysis of continuous-time fractional order uncertain systems. The first approach uses fractional order models with parametric uncertainty and robust stability of corresponding closed-loop control systems is investigated by using the value set concept in combination with the zero exclusion condition. On the other hand, the second approach is based on fractional order models with unstructured multiplicative uncertainty created by choosing a nominal plant and a suitable weight function. In this case, the graphical robust stability test utilizes the envelopes of the Nyquist diagrams. Both methods are illustrated by means of the joint example.