{"paper":{"title":"Backstepping Control of a Hyperbolic PDE System with Zero Characteristic Speed States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gustavo A. de Andrade, Iasson Karafyllis, Miroslav Krstic, Rafael Vazquez","submitted_at":"2022-11-25T18:46:46Z","abstract_excerpt":"While for coupled hyperbolic PDEs of first order there now exist numerous PDE backstepping designs, systems with zero speed, i.e., without convection but involving infinite-dimensional ODEs, which arise in many applications, from environmental engineering to lasers to manufacturing, have received virtually no attention. In this paper, we introduce single-input boundary feedback designs for a linear 1-D hyperbolic system with two counterconvecting PDEs and $n$ equations (infinite-dimensional ODEs) with zero characteristic speed. The inclusion of zero-speed states, which we refer to as {\\em atac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.14290","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/2211.14290/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"}