Exact Bounds for the Frequency Response of an Uncertain Plant with Ellipsoidal Perturbations

Abstract This paper deals with the frequency domain properties of an ellipsoidal family of rational functions, i.e. a family of rational functions whose coefficients depend affinely on an ellipsoidal parameter set. The problems considered are relevant to several recently developed techniques in the identification for control research area. The frequency plots of such a family are characterized and an efficient algorithm for computing the envelope of the Bode plots is devised. In particular, it is shown that the extremal values of the magnitude and phase of the value set at each frequency, which are in general non-convex optimization problems, can be computed via the solution of a sequence of Linear Matrix Inequalities (LMIs).