{"paper":{"title":"A note on approximating the nearest stable discrete-time descriptor system with fixed rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Michael Karow, Nicolas Gillis, Punit Sharma","submitted_at":"2018-07-12T08:56:20Z","abstract_excerpt":"Consider a discrete-time linear time-invariant descriptor system $Ex(k+1)=Ax(k)$ for $k \\in \\mathbb Z_{+}$. In this paper, we tackle for the first time the problem of stabilizing such systems by computing a nearby regular index one stable system $\\hat E x(k+1)= \\hat A x(k)$ with $\\text{rank}(\\hat E)=r$. We reformulate this highly nonconvex problem into an equivalent optimization problem with a relatively simple feasible set onto which it is easy to project. This allows us to employ a block coordinate descent method to obtain a nearby regular index one stable system. We illustrate the effective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04481","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/1807.04481/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"}