Moment matching-based model reduction for systems with linear quadratic output

In this paper, we present a time-domain moment matching approach for the model reduction of linear quadratic output (LQO) systems. The moment of an LQO system, is the output function of a projected state, based on the unique solution of a Sylvester equation. We determine a family of reduced-order parameterized models matching the given moment. First, we seek low-order approximations that preserve selected poles of a given LQO system. Secondly, we propose a gradient method to compute the parameters yielding the reduced order model that minimizes the ℋ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> error norm. Then, we address a mixed ℋ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> error norm-(partially) prescribed poles problem to obtain the approximation minimizing the ℋ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> error norm, in the class of reduced order models with prescribed poles. To solve the mixed problem, we propose a projected gradient method. Finally, the theory is illustrated on an LQO system of order thirty.