{"id":1158,"date":"2018-08-30T15:26:36","date_gmt":"2018-08-30T23:26:36","guid":{"rendered":"http:\/\/depts.washington.edu\/uwrainlab\/?page_id=1158"},"modified":"2018-08-30T15:26:36","modified_gmt":"2018-08-30T23:26:36","slug":"cartesian-products-on-z-matrix-networks-factorization-and-interval-analysis","status":"publish","type":"page","link":"http:\/\/depts.washington.edu\/uwrainlab\/cartesian-products-on-z-matrix-networks-factorization-and-interval-analysis\/","title":{"rendered":"Cartesian products on Z-Matrix networks: Factorization and interval analysis"},"content":{"rendered":"

A. Chapman, M. Mesbahi<\/strong><\/p>\n

International Symposium on Mathematical Theory of Networks and Systems<\/strong><\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

This chapter examines the relationship between the dynamics of large networks and of their smaller factor networks (factors) obtained through the factorization of the network\u2019s digraph representation. We specifically examine dynamics of networks which have Z-matrix state matrices. We perform a Cartesian product decomposition on its network structure producing factors which also have Z-matrix dynamics. A factorization lemma is presented that represents the trajectories of the large network in terms of the factors\u2019 trajectories. An interval matrix lemma provides families of network dynamics whose trajectories are bounded by the interval bounds\u2019 factors\u2019 trajectories.<\/p>\n<\/section>\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>\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

Links:<\/strong><\/p>\n

\"\"<\/a> \u00a0 \"\"<\/a> \u00a0 \"\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

A. Chapman, M. Mesbahi International Symposium on Mathematical Theory of Networks and Systems This chapter examines the relationship between the dynamics of large networks and of their smaller factor networks (factors) obtained through the factorization of the network\u2019s digraph representation. We specifically examine dynamics of networks which have Z-matrix state matrices. We perform a Cartesian […]<\/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\/1158"}],"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=1158"}],"version-history":[{"count":1,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1158\/revisions"}],"predecessor-version":[{"id":1159,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1158\/revisions\/1159"}],"wp:attachment":[{"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/media?parent=1158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}