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We investigate model order reduction (MOR) for linear dynamical systems,where a quadratic output is defined as a quantity of interest. The system canbe transformed into a linear dynamical system with many linear outputs. MOR isfeasible by the method of balanced truncation, but suffers from the largenumber of outputs in approximate methods. To ameliorate this shortcoming wederive an equivalent quadratic-bilinear system with a single linear output andanalyze the properties of this system. We examine MOR for this system via thetechnique of balanced truncation, which requires a stabilization of the system.Therein, the solution of two quadratic Lyapunov equations is traced back to thesolution of just two linear Lyapunov equations. We present numerical resultsfor several test examples comparing the two MOR approaches.

Balanced truncation for model order reduction of linear dynamical systems with quadratic outputs