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Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.<\/jats:p>","DOI":"10.1155\/2019\/9596253","type":"journal-article","created":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T03:24:39Z","timestamp":1554261879000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1748-2873","authenticated-orcid":false,"given":"Mohamed Karim","family":"Bouafoura","sequence":"first","affiliation":[]},{"given":"Naceur","family":"Benhadj Braiek","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,4,2]]},"reference":[{"volume-title":"Applied Theory of Functional Differential Equations","year":"1999","author":"Kolmanovskii V.","key":"e_1_2_10_1_2"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2014.10.413"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2016.1177132"},{"key":"e_1_2_10_4_2","doi-asserted-by":"crossref","unstructured":"KobayashiK. 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