OLIVI , Martine

The study of lossless matrices is motivated by two main applications in system theory: * Lossless matrices appear as cornerstone in matrix rational L2 approximation with stability constraint, * The transfer functions of conservative systems, and in particular scattering matrices of frequency filters, are lossless. The parametrizations that are...

This report deals with rational approximation of any specified order $n$ of transfer functions. Transfer functions are assumed to be matrices whose entries belong to the Hardy space for the complement of the closed unit disk endowed with the $L^2$-norm. A new approach is developed leading to an original algorithm, the first one to our knowledge...

This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius $L_2$-norm. We describe the topological structure of the set of approximants in terms of inner--unstable factorizations. This allows us to establish a...

The aim of this work is to generalize to the case of weighted $L^2$ spaces some results about $L^2$ approximation by analytic and rational functions which are useful to perform the identification of unknown transfer functions of stable (linear causal time--invariant) systems from incomplete frequency data.

We investigate the parametrization issue for discrete-time stable all-pass multivariable systems by means of a Schur algorithm involving a Nudelman interpolation condition. A recursive construction of balanced realizations is associated with it, that possesses a very good numerical behavior. Several atlases of charts or families of local...

Nous avons réalisé le bilan des émissions de gaz à effet de serre (GES) d'une équipe du centre de recherche Inria de Sophia Antipolis pour l'année 2019. L'équipe comprenait cette année-là 5 permanents, 5 doctorants, 1 post-doc, une assistante d'équipe à mi-temps et a accueilli pendant quelques mois deux stagiaires de master.

Lossless systems have many applications in systems and control theory, including signal processing, filter design, system identification , system approximation, and the parameterization of classes of linear systems. In this survey paper we address the issue of parameterization of the space of rational lossless matrix functions by successfully...

In Ober (1987) a balanced canonical form for continuous-time lossless systems was presented. This form has a tridiagonal dynamical matrix A and the useful property that the corresponding controllability matrix K is upper triangular. In this paper, a connection is established between Ober's canonical form and a Schur algorithm builts from...

Many normalizations in various classes of linear dynamical state-space systems lead to system representations which are determined up to a state isometry. Here we present a new set of techniques to obtain (local) canonical forms under state isometries, using what we call sub-diagonal pivot structures. These techniques lead to a very flexible,...

Symmetric inner rational functions naturally arise in the description of physical systems which satisfy the conservation and reciprocity laws. Inner matrix functions can be parametrized by a sequence of interpolation vectors obtained from a tangential Schur algorithm. In this paper, we present a Schur type algorithm which allows to describe...