Least squares moment matching-based model reduction using convex optimization

In this paper, we study the problem of time-domain least squares moment matching-based model order reduction of linear systems. We first present the definition and the charac-terization of a model of order
$r$
matching
$r\ll \nu$
moments of the given system. We then present the associated least squares moment matching problem in the form of a (nonconvex) optimization problem. Different from the existing results, we leave the interpolation points as decision variables and obtain an optimization problem with bilinear cost and constraints. The solution of the nonlinear least squares model reduction problem is computed at the optimal interpolation points using the efficient sequential convex programming algorithm. The proposed approach has practical advantages, since powerful convex optimization solvers, such as CVX, can be used to solve iteratively the optimization problem. A numerical example is given to illustrate the efficiency of our approach.