Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction

Abstract

Our aim is to numerically solve parameter-dependent Lyapunov equations using the reduced basis method. Such equations arise in parametric model order reduction. We restrict ourselves to the systems that affinely depend on the parameter, as our main strategy is the min-$\theta$ approach. In those cases, we derive various a posteriori error estimates. Based on these estimates, a greedy algorithm for constructing reduced bases is formulated. Thanks to the derived results, a novel so-called parametric balanced truncation model reduction method is developed. Numerical examples are presented.