{"paper":{"title":"Optimal Control and Stabilization Problem for Discrete-time Markov Jump Systems with Indefinite Weight Costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chunyan Han, Hongdan Li, Huanshui Zhang","submitted_at":"2018-03-20T06:22:28Z","abstract_excerpt":"It is well known that stability is the most fundamental nature with regard to a control system, in view of this, the stabilization becomes an inevitable control problem. This article mainly discusses the optimal control and stabilization problem for discrete-time systems involving Markov jump and multiplicative noise. The state and control weighting matrices in the cost function are allowed to be indefinite. By solving the forward-backward stochastic difference equations with Markov jump (FBSDEs-MJ) derived from the maximum principle, we conclude that the necessary and sufficient conditions of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07270","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"}