Second-order balanced truncation
TL;DR: A new method for constructing a reduced system by preserving the second-order structure of the original system is presented, using a variant of the well-known balanced truncation technique applied to second- order gramians.
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About: This article is published in Linear Algebra and its Applications. The article was published on 01 Jun 2006. and is currently open access. The article focuses on the topics: Truncation error (numerical integration) & Truncation.
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Citations
Balanced truncation model reduction of second-order systems
Timo Reis,Tatjana Stykel +1 more
TL;DR: This paper considers structure-preserving model reduction of second-order systems using a balanced truncation approach and shows that, in general, none of the existing structure- Preservingbalanced truncation methods for second- order systems preserves stability in the reduced models.
Structure Preserving Order Reduction of Large Scale Second Order Systems
TL;DR: For reduced order modelling of large scale second order systems while preserving the second order structure, two approaches based on matching some of the moments and/or Markov parameters of the transfer functions of the original and reduced systems are proposed.
115
Model Reduction of Interconnected Systems
Antoine Vandendorpe,Paul Van Dooren +1 more
- 01 Jan 2008
TL;DR: The purpose of this paper is to present both Krylov-based and Gramian-based model reduction techniques that preserve the structure of the interconnections in a reduced order system.
Model reduction of second order systems
Younes Chahlaoui,Kyle A. Gallivan,Antoine Vandendorpe,Paul Van Dooren +3 more
- 01 Jan 2005
TL;DR: Two classes of second order structure preserving model reduction techniques Krylov subspace-based and SVD-based are presented and conditions on the projectors that guarantee the reduced second order system tangentially interpolates the original system at given frequencies are derived.
An improved numerical method for balanced truncation for symmetric second-order systems
TL;DR: In this paper, the balanced truncation model order reduction for symmetric second-order systems is considered, where the large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method.
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Robust and Optimal Control
John Doyle
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TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
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All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†
TL;DR: In this paper, a complete characterization of all rational functions that minimize the Hankel-norm is derived, and the solution to the latter problem is via results on balanced realizations, all-pass functions and the inertia of matrices, all in terms of the solutions to Lyapunov equations.
3.1K
A collection of benchmark examples for model reduction of linear time invariant dynamical systems.
Younes Chahlaoui,Paul Van Dooren +1 more
- 01 Jan 2002
TL;DR: In order to test the numerical methods for model reduction, a benchmark collection is presented, which contain some useful real world examples reflecting current problems in applications.
Model reduction of second order systems
Younes Chahlaoui,Kyle A. Gallivan,Antoine Vandendorpe,Paul Van Dooren +3 more
- 01 Jan 2005
TL;DR: Two classes of second order structure preserving model reduction techniques Krylov subspace-based and SVD-based are presented and conditions on the projectors that guarantee the reduced second order system tangentially interpolates the original system at given frequencies are derived.