{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SO2S3UQABFVTTESLNJUFE5DYUA","short_pith_number":"pith:SO2S3UQA","canonical_record":{"source":{"id":"1511.01737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-05T13:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"d8c777c797717b833c0e86dfaa0b0691d7dce91e7f2fe1ab51db5ddd8f660732","abstract_canon_sha256":"0dc616133f9192476841f0f886a6ac357a32450605bbd9441a9ce57d43e1b0ed"},"schema_version":"1.0"},"canonical_sha256":"93b52dd200096b39924b6a68527478a035a5ad0e2527d6cd2ea596a3cb481e3f","source":{"kind":"arxiv","id":"1511.01737","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01737","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01737v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01737","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"SO2S3UQABFVT","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SO2S3UQABFVTTESL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SO2S3UQA","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SO2S3UQABFVTTESLNJUFE5DYUA","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-05T13:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"d8c777c797717b833c0e86dfaa0b0691d7dce91e7f2fe1ab51db5ddd8f660732","abstract_canon_sha256":"0dc616133f9192476841f0f886a6ac357a32450605bbd9441a9ce57d43e1b0ed"},"schema_version":"1.0"},"canonical_sha256":"93b52dd200096b39924b6a68527478a035a5ad0e2527d6cd2ea596a3cb481e3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:39.938207Z","signature_b64":"U/P3fwBpb5flQ/hfrX5KPa628qbIymOvSjefu5jD4mSeuHc4UE4ebJlos7MYsn0r5pI2T2Aka/B72UbxaaqkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93b52dd200096b39924b6a68527478a035a5ad0e2527d6cd2ea596a3cb481e3f","last_reissued_at":"2026-05-18T01:27:39.937735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:39.937735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01737","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vM1whhEoWA54k2emPoH5kM955KUTURhMMj4QrL9Q/bci/W2zfurGltdDG3AthKanwW3K+8Ayf9aflTQykQKQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:40:18.128645Z"},"content_sha256":"ebd15bbdbc67173529b33cb5360673ac1d00532e794902212a3a5f8657bb351d","schema_version":"1.0","event_id":"sha256:ebd15bbdbc67173529b33cb5360673ac1d00532e794902212a3a5f8657bb351d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SO2S3UQABFVTTESLNJUFE5DYUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Rate of Nonlinear Switched Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Philippe Jouan (LMRS), Sa\\\"id Naciri (LMRS)","submitted_at":"2015-11-05T13:43:12Z","abstract_excerpt":"This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions corresponding to that class of inputs converge arbitrarily slowly to the origin. Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01737","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FM/IxkKvidWdtj0RUcNWWZ816d35eXSk3D4QhDeCipdwtu0ex1e9JLB6TQshfvHaeg7vC0hNJwy0dDY6pPjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:40:18.129227Z"},"content_sha256":"8c029617bf33adb39a821e02659832683e7c38363b2ef991976d39999e11527b","schema_version":"1.0","event_id":"sha256:8c029617bf33adb39a821e02659832683e7c38363b2ef991976d39999e11527b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SO2S3UQABFVTTESLNJUFE5DYUA/bundle.json","state_url":"https://pith.science/pith/SO2S3UQABFVTTESLNJUFE5DYUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SO2S3UQABFVTTESLNJUFE5DYUA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T08:40:18Z","links":{"resolver":"https://pith.science/pith/SO2S3UQABFVTTESLNJUFE5DYUA","bundle":"https://pith.science/pith/SO2S3UQABFVTTESLNJUFE5DYUA/bundle.json","state":"https://pith.science/pith/SO2S3UQABFVTTESLNJUFE5DYUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SO2S3UQABFVTTESLNJUFE5DYUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SO2S3UQABFVTTESLNJUFE5DYUA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0dc616133f9192476841f0f886a6ac357a32450605bbd9441a9ce57d43e1b0ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-05T13:43:12Z","title_canon_sha256":"d8c777c797717b833c0e86dfaa0b0691d7dce91e7f2fe1ab51db5ddd8f660732"},"schema_version":"1.0","source":{"id":"1511.01737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01737","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01737v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01737","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"SO2S3UQABFVT","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SO2S3UQABFVTTESL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SO2S3UQA","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:8c029617bf33adb39a821e02659832683e7c38363b2ef991976d39999e11527b","target":"graph","created_at":"2026-05-18T01:27:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions corresponding to that class of inputs converge arbitrarily slowly to the origin. Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time.","authors_text":"Philippe Jouan (LMRS), Sa\\\"id Naciri (LMRS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-05T13:43:12Z","title":"Convergence Rate of Nonlinear Switched Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01737","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ebd15bbdbc67173529b33cb5360673ac1d00532e794902212a3a5f8657bb351d","target":"record","created_at":"2026-05-18T01:27:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0dc616133f9192476841f0f886a6ac357a32450605bbd9441a9ce57d43e1b0ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-05T13:43:12Z","title_canon_sha256":"d8c777c797717b833c0e86dfaa0b0691d7dce91e7f2fe1ab51db5ddd8f660732"},"schema_version":"1.0","source":{"id":"1511.01737","kind":"arxiv","version":1}},"canonical_sha256":"93b52dd200096b39924b6a68527478a035a5ad0e2527d6cd2ea596a3cb481e3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93b52dd200096b39924b6a68527478a035a5ad0e2527d6cd2ea596a3cb481e3f","first_computed_at":"2026-05-18T01:27:39.937735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:39.937735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/P3fwBpb5flQ/hfrX5KPa628qbIymOvSjefu5jD4mSeuHc4UE4ebJlos7MYsn0r5pI2T2Aka/B72UbxaaqkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:39.938207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebd15bbdbc67173529b33cb5360673ac1d00532e794902212a3a5f8657bb351d","sha256:8c029617bf33adb39a821e02659832683e7c38363b2ef991976d39999e11527b"],"state_sha256":"abcccc93c19d2820d9a38663856e565d3728143b1aace74c9b406919bda0d7b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LvLUcJ0dyxSfjLWHqDa8eDJiyoveizPZBTKMNf15T4O+15+V6zgYUsyB9vV+Rpzh0/K2VK66lC1Vy2BmSwt1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:40:18.131847Z","bundle_sha256":"ab306eed3596ed5271c993a3a84347e68a5a10be41626a839ebf018b30f1baa7"}}