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First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature. <\/jats:p>","DOI":"10.1177\/0142331220943071","type":"journal-article","created":{"date-parts":[[2020,8,4]],"date-time":"2020-08-04T11:44:31Z","timestamp":1596541471000},"page":"3168-3182","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming"],"prefix":"10.1177","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4380-1425","authenticated-orcid":false,"given":"Okan","family":"Demir","sequence":"first","affiliation":[{"name":"Electrical and Electronics Engineering, Bilkent University, Turkey"}]},{"given":"Hitay","family":"\u00d6zbay","sequence":"additional","affiliation":[{"name":"Electrical and Electronics Engineering, Bilkent University, Turkey"}]}],"member":"179","published-online":{"date-parts":[[2020,8,4]]},"reference":[{"key":"bibr1-0142331220943071","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.841922"},{"key":"bibr2-0142331220943071","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2015.0312"},{"key":"bibr3-0142331220943071","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2018.09.004"},{"key":"bibr4-0142331220943071","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1987.1104589"},{"volume-title":"Dynamic programming and optimal control. 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