Model reduction for linear parameter varying systems using scaled diagonal dominance

Abstract

A model-reduction method for linear, parameter-varying (LPV) systems based on parameter-varying balanced realizations is proposed. In general, this requires the solution of a large set of linear matrix inequalities, leading to numerical issues and high computational cost. It has been recognized recently that semidefinite optimization problems (SDP) can be cast into second order cone programs (SOCP) by replacing the positive definiteness constraints with stronger, scaled diagonal dominance conditions. Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large scale model reduction problems more efficiently. A numerical example is provided to demonstrate the efficiency of the approach.