Stability preservation for parametric model order reduction by matrix interpolation

A method to preserve stability in parametric model order reduction by matrix interpolation for the whole parameter range is proposed for high-order linear time-invariant systems. In the first step, system matrices of the high-dimensional parameter-dependent system are computed for a discrete set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method. Secondly, the reduced models are made contractive by solving low-dimensional Lyapunov equations. Thirdly, they are transformed into a consistent set of generalized coordinates for accurate interpolation results. These three steps are done offline and the matrices of the local systems are stored. Finally, a stable reduced order model for a new parameter vector can be calculated online by interpolating the precomputed matrices of the local low-dimensional models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications.