Stability analysis of incommensurate fractional systems based on interval arithmetics

The paper has several objectives. First of all, we recall some recent results for the determination of stability regions of irrational systems in the parametric space [1]. Then, we apply those results to the problem of investigating stability of fractional incommensurate systems in the parametric space. In essence we perform a stability-induced segmentation of the parametric space, so that transfer functions with parameters belonging to the same region are either all stable or all unstable. A robust estimation algorithm is formulated and solved using an algorithm of “prune and bound type”. The proposed method is applied on an illustrative numerical example and the results are confirmed through a root-locus analysis.