{"id":1138,"date":"2018-08-30T08:31:56","date_gmt":"2018-08-30T16:31:56","guid":{"rendered":"http:\/\/depts.washington.edu\/uwrainlab\/?page_id=1138"},"modified":"2018-08-30T08:31:56","modified_gmt":"2018-08-30T16:31:56","slug":"on-the-controllability-properties-of-circulant-networks","status":"publish","type":"page","link":"http:\/\/depts.washington.edu\/uwrainlab\/on-the-controllability-properties-of-circulant-networks\/","title":{"rendered":"On the Controllability Properties of Circulant Networks"},"content":{"rendered":"<p><strong>M. Nabi-Abdolyousefi, M. Mesbahi<\/strong><\/p>\n<p><strong>IEEE Transactions on Automatic Control<\/strong><\/p>\n<div class=\"gs_scl\">\n<div id=\"gsc_vcd_descr\" class=\"gsc_vcd_value\">\n<div class=\"row\">\n<div class=\"col ng-scope\">\n<div class=\"ng-scope\">\n<div class=\"abstract-text ng-binding\">\n<div class=\"row\">\n<div class=\"col ng-scope\">\n<div class=\"ng-scope\">\n<div class=\"abstract-text ng-binding\">\n<div class=\"row\">\n<div class=\"col ng-scope\">\n<div class=\"ng-scope\">\n<div class=\"abstract-text ng-binding\">\n<div class=\"row\">\n<div class=\"col ng-scope\">\n<div class=\"ng-scope\">\n<div class=\"abstract-text ng-binding\">\n<div class=\"row\">\n<div class=\"col ng-scope\">\n<div class=\"ng-scope\">\n<div class=\"abstract-text ng-binding\">This paper examines the controllability of a group of first order agents, adopting a weighted consensus-type coordination protocol over a circulant network. Specifically, it is shown that a circulant network with Laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes. Our approach leverages on the Cauchy-Binet formula, which in conjunction with the Popov-Belevitch-Hautus test, leads to new insights on structural aspects of network controllability.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"gs_scl\"><\/div>\n<p><strong>Links:<\/strong><\/p>\n<p><a href=\"https:\/\/ieeexplore.ieee.org\/document\/6507614\/\"><img loading=\"lazy\" class=\"alignnone wp-image-810\" src=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/download.png\" alt=\"\" width=\"26\" height=\"26\" srcset=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/download.png 225w, http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/download-150x150.png 150w\" sizes=\"(max-width: 26px) 100vw, 26px\" \/><\/a> \u00a0 <a href=\"https:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=6507614\"><img loading=\"lazy\" class=\"alignnone wp-image-811\" src=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/image_preview.png\" alt=\"\" width=\"31\" height=\"31\" srcset=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/image_preview.png 250w, http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/image_preview-150x150.png 150w\" sizes=\"(max-width: 31px) 100vw, 31px\" \/><\/a> \u00a0 <a href=\"https:\/\/scholar.google.com\/scholar?hl=en&amp;as_sdt=0%2C48&amp;q=On+the+Controllability+Properties+of+Circulant+Networks&amp;btnG=#d=gs_cit&amp;p=&amp;u=%2Fscholar%3Fq%3Dinfo%3ANdxwqb9L3fYJ%3Ascholar.google.com%2F%26output%3Dcite%26scirp%3D0%26hl%3Den\"><img loading=\"lazy\" class=\"alignnone wp-image-809\" src=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-300x97.png\" alt=\"\" width=\"65\" height=\"21\" srcset=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-300x97.png 300w, http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-768x248.png 768w, http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-1024x330.png 1024w, http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_.png 1200w\" sizes=\"(max-width: 65px) 100vw, 65px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>M. Nabi-Abdolyousefi, M. Mesbahi IEEE Transactions on Automatic Control This paper examines the controllability of a group of first order agents, adopting a weighted consensus-type coordination protocol over a circulant network. Specifically, it is shown that a circulant network with Laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes. Our approach leverages [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1138"}],"collection":[{"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/comments?post=1138"}],"version-history":[{"count":1,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1138\/revisions"}],"predecessor-version":[{"id":1139,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1138\/revisions\/1139"}],"wp:attachment":[{"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/media?parent=1138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}