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We formulate here an approach to model reduction that is well-suited for linear time-invariant control systems that are stabilizable and detectable but may otherwise be unstable. We introduce a modified $mathcal{H}_2$-error metric, the $mathcal{H}_2$-gap, that provides an effective measure of model fidelity in this setting. While the direct evaluation of the $mathcal{H}_2$-gap requires the solutions of a pair of algebraic Riccati equations associated with related closed-loop systems, we are able to work entirely within an interpolatory framework, developing algorithms and supporting analysis that do not reference full-order closed-loop Gramians. This leads to a computationally effective strategy yielding reduced models designed so that the corresponding reduced closed-loop systems will interpolate the full-order closed-loop system at specially adapted interpolation points, without requiring evaluation of the full-order closed-loop system nor even computation of the feedback law that determines it. The analytical framework and computational algorithm presented here provides an effective new approach toward constructing reduced-order models for unstable systems. Numerical examples for an unstable convection diffusion equation and a linearized incompressible Navier-Stokes equation illustrate the effectiveness of this approach.
In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric bilinear sys
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the vector of param
We propose a general --- i.e., independent of the underlying equation --- registration method for parameterized Model Order Reduction. Given the spatial domain $Omega subset mathbb{R}^d$ and a set of snapshots ${ u^k }_{k=1}^{n_{rm train}}$ over $Ome
In an iterative approach for solving linear systems with ill-conditioned, symmetric positive definite (SPD) kernel matrices, both fast matrix-vector products and fast preconditioning operations are required. Fast (linear-scaling) matrix-vector produc
We propose a projection-based monolithic model order reduction (MOR) procedure for a class of problems in nonlinear mechanics with internal variables. The work is is motivated by applications to thermo-hydro-mechanical (THM) systems for radioactive w