Frequency-Domain Identification of Discrete-Time Systems using Sum-of-Rational Optimization

We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem whose objective function is the sum of weighted squared residuals at each observed frequency datapoint. Stability is enforced using a polynomial matrix inequality constraint. The problem is solved globally by a moment-sum-of-squares hierarchy of semidefinite programs through a framework for sum-of-rational-functions optimization. Convergence of the moment-sum-of-squares program is guaranteed as the bound on the degree of the sum-of-squares polynomials approaches infinity. The performance of the proposed method is demonstrated using numerical simulation examples.