Stability Preservation in Model Order Reduction of Linear Dynamical Systems

We examine projection-based model order reduction of Galerkin-type for linear dynamical systems. In the case of ordinary differential equations, a transformation of the original system guarantees that any reduced system inherits asymptotic stability. The transformation matrix satisfies a high-dimensional Lyapunov equation. We use a frequency domain approach, where the solution of the Lyapunov equation represents a matrix-valued integral. Consequently, quadrature methods yield approximations in numerical computations. In the case of differential-algebraic equations, the stabilization technique is applicable via a regularization. We present numerical results for a test example.