Computation of Stability Margins for Uncertain Linear Fractional-order Systems using Interval Constraint Propagation

Abstract

The present paper proposes an algorithm for finding the stability margins and cross over frequencies for an uncertain fractional-order system using interval constraint propagation technique. It is first shown that the problem of finding the stability margins and crossover frequencies can be formulated as a interval constraint satisfaction problem and then solved using branch and prune algorithm. The algorithm guarantees that the stability margins and the crossover frequencies are computed to prescribed accuracy and that theses values are reliable in the face of all kinds of computational errors. The other advantage of the method is that the stability margins and crossover frequencies can be computed without the need of frequency response plots or any kind of approximations. Two examples of uncertain fractional-order systems are taken from the literature and their stability margins and crossover frequencies are computed using the proposed algorithm.