Nu-gap metric a sum-of-squares and linear matrix inequality approach

The nu-gap metric represents a good measure of the distance between systems in a closed-loop setting. The purpose of this paper is to present a novel method to compute the nu-gap using a Semi-Definite Programming (SDP) procedure. Our approach is formulated through a three-step modus operandi: (i) first an initial central transfer function is computed through Linear Matrix Inequality (LMI) relaxations of a nonconvex problem, on the basis of matrix Sum-Of-Squares (SOS) decompositions, followed by (ii) a non-linear LMI-based refinement, and finally (iii) the actual computation of the nu-gap using the Kalman-Yakubovich-Popov (KYP) Lemma. We illustrate the practicality of the proposed method on numerical examples.