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We consider second-order linear time-invariant systems. The objective of this paper is to present a new method for constructing a reduced system by preserving the second-order structure of the original system. This new model reduction method uses a variant of the well-known balanced truncation technique applied to second-order gramians. We also compare it… (More)

This paper presents new recursive projection techniques to compute reduced order models of time-varying linear systems. The methods produce a lowrank approximation of the gramians or of the Hankel map of the system and are mainly based on matrix operations that can exploit sparsity of the model. We show the practical relevance of our results with a few… (More)

- Y. Chahlaoui, Kyle A. Gallivan, Paul Van Dooren
- SIAM J. Matrix Analysis Applications
- 2003

In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram–Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices… (More)

In this note we present a new updating technique to estimate a low rank approximation of the Hankel map of a time-varying system. We obtain error estimates of our approximation and also explain how to use this for model reduction of time-varying as well as time invariant systems.

where the matrix M ∈ RN×N is assumed to be invertible. Models of mechanical systems are often of this type since (1.1) then represents the equation of motion of the system. For such a system M = MT , C = CT and K = KT are respectively the mass, damping and stiffness matrices, f(t) ∈ RN×1 is the vector of external forces, and x(t) ∈ RN×1 is the vector of… (More)

In this paper we present a Smith-like updating technique to estimate a low rank approximation of the Gramians of a time-varying system. We obtain error estimates of our approximation and also explain how to use this for model reduction of time-varying systems.

- Y. Chahlaoui, Kyle A. Gallivan, +4 authors Paul Van Dooren
- 2005

We describe an algorithm for estimating the H∞-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of theH∞-norm and then uses extrapolation to improve these estimates. Résumé. Nous décrivons un algorithme pour estimer la norme H∞ d’un… (More)

- Xugang Ye, Steve Blumsack, Y. Chahlaoui, R. N. Braswell
- 2012

In this paper, we construct a global optimization algorithm to compute the H∞ norm of the transfer matrix of linear dynamic system. The algorithm takes the benefit of the fact that the generalized eigenvalue problem with Hamiltonian or symplectic structure not only gives a finite number of sets of subintervals of real axis among which the global maximum of… (More)

We describe an algorithm for estimating the H∞-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of theH∞-norm and then uses extrapolation to improve these estimates. Résumé. Nous décrivons un algorithme pour estimer la norme H∞ d’un… (More)

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