Christopher A. Beattie

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The optimal H 2 model reduction problem is of great importance in the area of dy-namical systems and simulation. In the literature, two independent frameworks have evolved focusing either on solution of Lyapunov equations on the one hand or interpolation of transfer functions on the other, without any apparent connection between the two approaches. In this(More)
— Unstable dynamical systems can be viewed from a variety of perspectives. We discuss the potential of an input-output map associated with an unstable system to represent a bounded map from L2(R) to itself and then develop criteria for optimal reduced order approximations to the original (unstable) system with respect to an L2-induced Hilbert-Schmidt norm.(More)
We provide a unifying projection-based framework for structure-preserving interpo-latory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model.(More)
The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of(More)
— We present a trust-region approach for optimal H2 model reduction of multiple-input/multiple-output (MIMO) linear dynamical systems. The proposed approach generates a sequence of reduced order models producing monotone improving H2 error norms and is globally convergent to a reduced order model guaranteed to satisfy first-order optimality conditions with(More)
Krylov subspace methods have proved effective for many non-Hermitian eigenvalue problems, yet the analysis of such algorithms is involved. Convergence can be characterized by the angle the approximating subspace forms with a desired invariant subspace, resulting in a geometric framework that is robust to eigenvalue ill-conditioning. This paper describes a(More)
We present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization C(s) (s) −1 B(s) + D. This includes rational Krylov-based interpolation methods as a special case. The broader framework allows retention of special structure in reduced models such as symmetry, second-and higher order structure, state(More)
— Port network modeling of physical systems leads directly to an important class of passive state space systems: port-Hamiltonian systems. We consider here methods for model reduction of large scale port-Hamiltonian systems that preserve port-Hamiltonian structure and are capable of yielding reduced order models that satisfy first-order optimality(More)
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced-order model not only is a(More)