Y. Chahlaoui

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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)
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)
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)
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)
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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