{"id":1030,"date":"2018-08-22T17:37:04","date_gmt":"2018-08-23T01:37:04","guid":{"rendered":"http:\/\/depts.washington.edu\/uwrainlab\/?page_id=1030"},"modified":"2018-08-23T16:45:40","modified_gmt":"2018-08-24T00:45:40","slug":"multiple-time-scales-in-network-of-networks","status":"publish","type":"page","link":"http:\/\/depts.washington.edu\/uwrainlab\/multiple-time-scales-in-network-of-networks\/","title":{"rendered":"Multiple Time-Scales in Network-of-Networks"},"content":{"rendered":"

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

IEEE American Control Conference<\/strong><\/p>\n

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This paper examines a multiple time-scale system where each layer of time-scale dynamics corresponds to a network. Coupling between layers induces a network-of-networks dynamic system. Assuming a hierarchical interaction structure between network time-scale layers with sufficient time-scale differences, layers can be studied under a separation principle. We describe stability of the network-of-networks through a composite Lyapunov function and provide a bilinear matrix inequality condition to guarantee asymptotic stability. Techniques are proposed to adapt this inequality into a linear matrix inequality condition making it computationally efficient to solve as a convex optimization problem. We examine estimates of the dynamics’ domain of attraction and provide conservative bounds on the time-scale separation required to guarantee stability. A class of network-of-networks dynamics with modified consensus dynamics and a state-dependent network structure is then explored. Graph-based guarantees are provided that certify the stability of the system with the worst case rate of convergence dictating conservative bounds on the time-scale separation. An illustrative network-of-networks example is presented.<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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A. Chapman, M. Mesbahi IEEE American Control Conference This paper examines a multiple time-scale system where each layer of time-scale dynamics corresponds to a network. Coupling between layers induces a network-of-networks dynamic system. Assuming a hierarchical interaction structure between network time-scale layers with sufficient time-scale differences, layers can be studied under a separation principle. We […]<\/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\/1030"}],"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=1030"}],"version-history":[{"count":3,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1030\/revisions"}],"predecessor-version":[{"id":1096,"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/1030\/revisions\/1096"}],"wp:attachment":[{"href":"http:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/media?parent=1030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}