{"paper":{"title":"Optimization of the $H_\\infty$-norm of Dynamic Flow Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Johansson, Henrik Sandberg, Jie Chen, Jieqiang Wei, Karl H. Johansson","submitted_at":"2017-10-09T15:41:24Z","abstract_excerpt":"In this paper, we study the $H_\\infty$-norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the $H_\\infty$-norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the $H_\\infty$-norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the $H_\\infty$-norm, which is in terms of the algebraic connectivity of the graph o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03154","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}