{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:GAVOMX3I5YBKGIT2IH63QIEIXU","short_pith_number":"pith:GAVOMX3I","schema_version":"1.0","canonical_sha256":"302ae65f68ee02a3227a41fdb82088bd12bfb35b5abe6b95a76f44b964befb4a","source":{"kind":"arxiv","id":"0901.1842","version":2},"attestation_state":"computed","paper":{"title":"Small gain theorems for large scale systems and construction of ISS Lyapunov functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bj\\\"orn S. R\\\"uffer, Fabian R. Wirth, Sergey N. Dashkovskiy","submitted_at":"2009-01-13T17:49:42Z","abstract_excerpt":"We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a gener"},"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":"0901.1842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-01-13T17:49:42Z","cross_cats_sorted":[],"title_canon_sha256":"fc6885b3b49f4e272a9b3f0cbeb46afad0fcd60ac35957ccf2e25fd18aa42632","abstract_canon_sha256":"b67db22a465e4ff635209205d3917ceab3b53c58c0145e1698d066d711b2251a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:06.029992Z","signature_b64":"GDhd+e2FrXXus0t8Spypxk2KpcDVIZ84SXUYjjgAHdXa+5no/FZUslHYnU2/efFVPuj0C2iqWvVnodI+FxdXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"302ae65f68ee02a3227a41fdb82088bd12bfb35b5abe6b95a76f44b964befb4a","last_reissued_at":"2026-05-18T04:41:06.029536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:06.029536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small gain theorems for large scale systems and construction of ISS Lyapunov functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bj\\\"orn S. R\\\"uffer, Fabian R. Wirth, Sergey N. Dashkovskiy","submitted_at":"2009-01-13T17:49:42Z","abstract_excerpt":"We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1842","kind":"arxiv","version":2},"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":"0901.1842","created_at":"2026-05-18T04:41:06.029615+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.1842v2","created_at":"2026-05-18T04:41:06.029615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1842","created_at":"2026-05-18T04:41:06.029615+00:00"},{"alias_kind":"pith_short_12","alias_value":"GAVOMX3I5YBK","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"GAVOMX3I5YBKGIT2","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"GAVOMX3I","created_at":"2026-05-18T12:25:59.703012+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/GAVOMX3I5YBKGIT2IH63QIEIXU","json":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU.json","graph_json":"https://pith.science/api/pith-number/GAVOMX3I5YBKGIT2IH63QIEIXU/graph.json","events_json":"https://pith.science/api/pith-number/GAVOMX3I5YBKGIT2IH63QIEIXU/events.json","paper":"https://pith.science/paper/GAVOMX3I"},"agent_actions":{"view_html":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU","download_json":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU.json","view_paper":"https://pith.science/paper/GAVOMX3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.1842&json=true","fetch_graph":"https://pith.science/api/pith-number/GAVOMX3I5YBKGIT2IH63QIEIXU/graph.json","fetch_events":"https://pith.science/api/pith-number/GAVOMX3I5YBKGIT2IH63QIEIXU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU/action/storage_attestation","attest_author":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU/action/author_attestation","sign_citation":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU/action/citation_signature","submit_replication":"https://pith.science/pith/GAVOMX3I5YBKGIT2IH63QIEIXU/action/replication_record"}},"created_at":"2026-05-18T04:41:06.029615+00:00","updated_at":"2026-05-18T04:41:06.029615+00:00"}