{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:7ROYNWM52A5AG7MZSTRK6UKZL3","short_pith_number":"pith:7ROYNWM5","schema_version":"1.0","canonical_sha256":"fc5d86d99dd03a037d9994e2af51595ee5dc4375a72f035a4d24afac1d499197","source":{"kind":"arxiv","id":"math/0301335","version":1},"attestation_state":"computed","paper":{"title":"Persistency of excitation for uniform convergence in nonlinear control systems","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Andrew R. Teel, Antonio Loria, Dobrivoje Popovic, Elena Panteley","submitted_at":"2003-01-28T18:22:05Z","abstract_excerpt":"In previous papers we have introduced a sufficient condition for uniform attractivity of the origin for a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform delta-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u-delta-PE which is conceptually similar to but technically different from its predecesso"},"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":"math/0301335","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2003-01-28T18:22:05Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"2e17b585b7c5eb299158a14818baab1ad428d687c3e3a529ef10325dd6e265fe","abstract_canon_sha256":"172945d90b0c9176eb56611e5698e6d3990c8ec206bc0a80b3cf31a3f32241eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:55.571161Z","signature_b64":"enm3Nnqx6hhTNf93PLt4mnEuEnd1FxdHgrLkxQwiErtdThS/SZewITSsOkqSA0JReWvST5xLCau31ZCj8XwhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5d86d99dd03a037d9994e2af51595ee5dc4375a72f035a4d24afac1d499197","last_reissued_at":"2026-07-04T14:36:55.570776Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:55.570776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Persistency of excitation for uniform convergence in nonlinear control systems","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Andrew R. Teel, Antonio Loria, Dobrivoje Popovic, Elena Panteley","submitted_at":"2003-01-28T18:22:05Z","abstract_excerpt":"In previous papers we have introduced a sufficient condition for uniform attractivity of the origin for a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform delta-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u-delta-PE which is conceptually similar to but technically different from its predecesso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301335","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0301335/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0301335","created_at":"2026-07-04T14:36:55.570836+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0301335v1","created_at":"2026-07-04T14:36:55.570836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301335","created_at":"2026-07-04T14:36:55.570836+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ROYNWM52A5A","created_at":"2026-07-04T14:36:55.570836+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ROYNWM52A5AG7MZ","created_at":"2026-07-04T14:36:55.570836+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ROYNWM5","created_at":"2026-07-04T14:36:55.570836+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.04062","citing_title":"On Sufficient Richness for Linear Time-Invariant Systems","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3","json":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3.json","graph_json":"https://pith.science/api/pith-number/7ROYNWM52A5AG7MZSTRK6UKZL3/graph.json","events_json":"https://pith.science/api/pith-number/7ROYNWM52A5AG7MZSTRK6UKZL3/events.json","paper":"https://pith.science/paper/7ROYNWM5"},"agent_actions":{"view_html":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3","download_json":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3.json","view_paper":"https://pith.science/paper/7ROYNWM5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0301335&json=true","fetch_graph":"https://pith.science/api/pith-number/7ROYNWM52A5AG7MZSTRK6UKZL3/graph.json","fetch_events":"https://pith.science/api/pith-number/7ROYNWM52A5AG7MZSTRK6UKZL3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3/action/storage_attestation","attest_author":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3/action/author_attestation","sign_citation":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3/action/citation_signature","submit_replication":"https://pith.science/pith/7ROYNWM52A5AG7MZSTRK6UKZL3/action/replication_record"}},"created_at":"2026-07-04T14:36:55.570836+00:00","updated_at":"2026-07-04T14:36:55.570836+00:00"}