Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output

Balanced truncation is a widely used and appreciated projection‐based model reduction technique for linear systems. This technique has the following two important properties: approximations by balanced truncation preserve the stability and the H∞‐norm (the maximum of the frequency response) of the error system is bounded above by twice the sum of the neglected singular values. This paper tries to extend the framework of linear balanced truncation to systems with a quadratic output. For such systems, the controllability Gramian remains the same. The observability Gramian is computed from a linear system with multiple outputs that is derived from the quadratic output of the original system. We give a numerical example for a large‐scale system arising from structural analysis.