Interval-Based Verification Techniques for the Analysis of Uncertain Fractional-Order System Models

Fractional-order differential equations are applied in many fields of engineering as well as computational physics to describe dynamic phenomena which are characterized by that fact that an infinitely long horizon of past state values influences the evolution of future states. Moreover, from the perspective of a frequency-domain analysis, these types of system models show the property that even in the case of linear dynamics, the associated amplitude responses are no longer characterized by slopes which are integer multiples of ±20dB per frequency decade or, respectively, multiples of ±π/2 in the corresponding phase response. Although the development of simulation routines for fractional-order models with point-valued parameters and initial conditions has received large attention in recent years, the robustness analysis of such system models with respect to interval uncertainty has not yet been considered widely. Therefore, this paper aims at bridging the gap between already existing verified simulation techniques for integer-order models with uncertain parameters and the respective fractional counterparts, both from the points of view of the necessary methodological background and from the perspective of a representative test example.