{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VZY27VGYP7EG4HNN3EVD5DFA2E","short_pith_number":"pith:VZY27VGY","schema_version":"1.0","canonical_sha256":"ae71afd4d87fc86e1dadd92a3e8ca0d13fe1da86c6a2203ca5f5def93b5b8141","source":{"kind":"arxiv","id":"1905.05854","version":1},"attestation_state":"computed","paper":{"title":"On Structured Lyapunov Functions and Dissipativity in Interconnected LTI Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Andrej Joki\\'c, Ivica Naki\\'c","submitted_at":"2019-05-14T21:42:26Z","abstract_excerpt":"In this paper we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network, composed as a set of linear time invariant (LTI) systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the individual systems in the network are dissipative with respect to a (nonempty) set of interconnection neutral supply functions. Each supply function from this set is defined on a single interconnection link in th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.05854","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2019-05-14T21:42:26Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"590a6ea084f814ed56f987d1021a28385ae4bc8703e94210e1a0fe6cf742dab7","abstract_canon_sha256":"b9d9a15b5d21dbbb9e29993e864a9a265ba5ef7c25ccc00d037bcd9ff278df46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:08.297765Z","signature_b64":"WzX30hWjnrP0iHjFcjnAEJDP7MKR444c2rnHnBnCJq/KwAVdCr8akKyvs8sVucp9/YdbRarLskJQboPld1VBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae71afd4d87fc86e1dadd92a3e8ca0d13fe1da86c6a2203ca5f5def93b5b8141","last_reissued_at":"2026-05-17T23:46:08.297019Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:08.297019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Structured Lyapunov Functions and Dissipativity in Interconnected LTI Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Andrej Joki\\'c, Ivica Naki\\'c","submitted_at":"2019-05-14T21:42:26Z","abstract_excerpt":"In this paper we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network, composed as a set of linear time invariant (LTI) systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the individual systems in the network are dissipative with respect to a (nonempty) set of interconnection neutral supply functions. Each supply function from this set is defined on a single interconnection link in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05854","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.05854","created_at":"2026-05-17T23:46:08.297127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.05854v1","created_at":"2026-05-17T23:46:08.297127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05854","created_at":"2026-05-17T23:46:08.297127+00:00"},{"alias_kind":"pith_short_12","alias_value":"VZY27VGYP7EG","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VZY27VGYP7EG4HNN","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VZY27VGY","created_at":"2026-05-18T12:33:30.264802+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E","json":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E.json","graph_json":"https://pith.science/api/pith-number/VZY27VGYP7EG4HNN3EVD5DFA2E/graph.json","events_json":"https://pith.science/api/pith-number/VZY27VGYP7EG4HNN3EVD5DFA2E/events.json","paper":"https://pith.science/paper/VZY27VGY"},"agent_actions":{"view_html":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E","download_json":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E.json","view_paper":"https://pith.science/paper/VZY27VGY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.05854&json=true","fetch_graph":"https://pith.science/api/pith-number/VZY27VGYP7EG4HNN3EVD5DFA2E/graph.json","fetch_events":"https://pith.science/api/pith-number/VZY27VGYP7EG4HNN3EVD5DFA2E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E/action/storage_attestation","attest_author":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E/action/author_attestation","sign_citation":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E/action/citation_signature","submit_replication":"https://pith.science/pith/VZY27VGYP7EG4HNN3EVD5DFA2E/action/replication_record"}},"created_at":"2026-05-17T23:46:08.297127+00:00","updated_at":"2026-05-17T23:46:08.297127+00:00"}