{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FVO73JPEESG2ROU5YEAW7HFZ32","short_pith_number":"pith:FVO73JPE","schema_version":"1.0","canonical_sha256":"2d5dfda5e4248da8ba9dc1016f9cb9de87c9a84c619daf457253c3f5fdcb0a45","source":{"kind":"arxiv","id":"1710.03710","version":5},"attestation_state":"computed","paper":{"title":"LaSalle Invariance Principle for Discrete-time Dynamical Systems: A Concise and Self-contained Tutorial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.OC"],"primary_cat":"math.DS","authors_text":"Francesco Bullo, Wenjun Mei","submitted_at":"2017-10-10T16:31:09Z","abstract_excerpt":"LaSalle invariance principle was originally proposed in the 1950's and has become a fundamental mathematical tool in the area of dynamical systems and control. In both theoretical research and engineering practice, discrete-time dynamical systems have been at least as extensively studied as continuous-time systems. For example, model predictive control is typically studied in discrete-time via Lyapunov methods. However, there is a peculiar absence in the standard literature of standard treatments of Lyapunov functions and LaSalle invariance principle for discrete-time nonlinear systems. Most o"},"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":"1710.03710","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T16:31:09Z","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"title_canon_sha256":"ce749ce8d08d681637ee7a57ce30743cd85fa595260ac9eb67536aef118bac70","abstract_canon_sha256":"a04c8e2d5e132a2cdaaeadf9d9729f40673cefb270c17306293444892986a4bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:04.648523Z","signature_b64":"/T6g9aFAa4sNpAu/CT/nXmdXM/nZXpaKnFG1SjXM9Js9A3Gw5fmqkmvzpQRKgNz3kvyaXFVPOmYvIicaE+whBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d5dfda5e4248da8ba9dc1016f9cb9de87c9a84c619daf457253c3f5fdcb0a45","last_reissued_at":"2026-06-04T19:11:04.648071Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:04.648071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"LaSalle Invariance Principle for Discrete-time Dynamical Systems: A Concise and Self-contained Tutorial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.OC"],"primary_cat":"math.DS","authors_text":"Francesco Bullo, Wenjun Mei","submitted_at":"2017-10-10T16:31:09Z","abstract_excerpt":"LaSalle invariance principle was originally proposed in the 1950's and has become a fundamental mathematical tool in the area of dynamical systems and control. In both theoretical research and engineering practice, discrete-time dynamical systems have been at least as extensively studied as continuous-time systems. For example, model predictive control is typically studied in discrete-time via Lyapunov methods. However, there is a peculiar absence in the standard literature of standard treatments of Lyapunov functions and LaSalle invariance principle for discrete-time nonlinear systems. Most o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03710","kind":"arxiv","version":5},"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/1710.03710/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":"1710.03710","created_at":"2026-06-04T19:11:04.648134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.03710v5","created_at":"2026-06-04T19:11:04.648134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03710","created_at":"2026-06-04T19:11:04.648134+00:00"},{"alias_kind":"pith_short_12","alias_value":"FVO73JPEESG2","created_at":"2026-06-04T19:11:04.648134+00:00"},{"alias_kind":"pith_short_16","alias_value":"FVO73JPEESG2ROU5","created_at":"2026-06-04T19:11:04.648134+00:00"},{"alias_kind":"pith_short_8","alias_value":"FVO73JPE","created_at":"2026-06-04T19:11:04.648134+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/FVO73JPEESG2ROU5YEAW7HFZ32","json":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32.json","graph_json":"https://pith.science/api/pith-number/FVO73JPEESG2ROU5YEAW7HFZ32/graph.json","events_json":"https://pith.science/api/pith-number/FVO73JPEESG2ROU5YEAW7HFZ32/events.json","paper":"https://pith.science/paper/FVO73JPE"},"agent_actions":{"view_html":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32","download_json":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32.json","view_paper":"https://pith.science/paper/FVO73JPE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.03710&json=true","fetch_graph":"https://pith.science/api/pith-number/FVO73JPEESG2ROU5YEAW7HFZ32/graph.json","fetch_events":"https://pith.science/api/pith-number/FVO73JPEESG2ROU5YEAW7HFZ32/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32/action/storage_attestation","attest_author":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32/action/author_attestation","sign_citation":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32/action/citation_signature","submit_replication":"https://pith.science/pith/FVO73JPEESG2ROU5YEAW7HFZ32/action/replication_record"}},"created_at":"2026-06-04T19:11:04.648134+00:00","updated_at":"2026-06-04T19:11:04.648134+00:00"}