{"id":84,"date":"2015-10-01T14:25:01","date_gmt":"2015-10-01T12:25:01","guid":{"rendered":"https:\/\/project.inria.fr\/rarl2\/?page_id=84"},"modified":"2016-10-01T19:22:35","modified_gmt":"2016-10-01T17:22:35","slug":"presentation","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/rarl2\/","title":{"rendered":"Presentation"},"content":{"rendered":"<p>RARL2 is a matlab toolbox. Its goal is to provide\u00a0 a <strong>stable<\/strong> rational L<sup>2 <\/sup> -approximation of <strong>prescribed order<\/strong> to a\u00a0 H<sup>2<\/sup> <strong>matrix-valued<\/strong> function\u00a0 given in one of the following forms<\/p>\n<ul>\n<li>a finite number of Fourier coefficients<\/li>\n<li>a state-space realization<\/li>\n<li>sampled values on the unit circle (frequency data).<\/li>\n<\/ul>\n<p>It can be used for <strong> model reduction, identification from frequency data, pole recovery<\/strong>.\u00a0It works for  <b>MIMO<\/b> systems.<br \/>\nThe optimization method is based on the following points<\/p>\n<ul>\n<li> the optimization range is reduced to a compact set<\/li>\n<li> a parametrization of stable all-pass systems is used which guarantees:\n<ul>\n<li> <b>stability <\/b> of the approximant<\/li>\n<li> degree control <\/li>\n<li> well-conditionning <\/li>\n<\/ul>\n<\/ul>\n<h3>Related publications<\/h3>\n<ul>\n<li>M. Olivi, F. Seyfert, J.P. Marmorat,  <a href=\" http:\/\/www-sop.inria.fr\/members\/Martine.Olivi\/Papiers\/AUTO_MOSfinal.pdf\"> Identication of microwave  filters by analytic and rational H<sup>2<\/sup>approximation, <\/a><i>Automatica, <\/i> 49(2013) 317-325<\/li>\n<li>J.P. Marmorat, M. Olivi, <a href=\" http:\/\/www-sop.inria.fr\/members\/Martine.Olivi\/Papiers\/Nudelman_r2.pdf\"> Nudelman Interpolation, Parametrization of Lossless Functions and balanced realizations, <\/a><i>Automatica, <\/i> 43 (2007), 1329-1338<\/li>\n<li>B. Hanzon, M. Olivi, R.L.M. Peeters, <a href=\"http:\/\/www-sop.inria.fr\/members\/Martine.Olivi\/Papiers\/HOP2005.pdf\"> Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm, <\/a><i>Linear Algebra and its Applications, <\/i> 418 (2006), 793-820<\/li>\n<li>J.P. Marmorat, M. Olivi, B. Hanzon, R. Peeters, <a href=\"http:\/\/www-sop.inria.fr\/members\/Martine.Olivi\/Papiers\/MOHP_CDC02.pdf\"> Matrix rational H2-approximation: a state-space approach using Schur parameters <\/a>, <i> CDC02 (Las Vegas)<\/i> <a href=\"http:\/\/www-sop.inria.fr\/members\/Martine.Olivi\/Papiers\/CDC02s.pdf\"> Slides of the presentation <\/a><\/li>\n<li>D. Alpay, L. Baratchart, A. Gombani, On the differential structure of matrix-valued rational inner functions, <i>Operator Theory: Advances and Applications, <\/i> 73 (1994), 30&#8211;66<\/li>\n<li>L. Baratchart, M. Cardelli, M. Olivi, Identification and rational L2 approximation: a gradient algorithm, <i> Automatica<\/i> 27(2) (1991), 413-418<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>RARL2 is a matlab toolbox. Its goal is to provide\u00a0 a stable rational L2 -approximation of prescribed order to a\u00a0 H2 matrix-valued function\u00a0 given in one of the following forms a finite number of Fourier coefficients a state-space realization sampled values on the unit circle (frequency data). It can be\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/rarl2\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":40,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-84","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/users\/40"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/comments?post=84"}],"version-history":[{"count":18,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/84\/revisions"}],"predecessor-version":[{"id":151,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/84\/revisions\/151"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/media?parent=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}