{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:19:47Z","timestamp":1746803987183,"version":"3.40.5"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61273008"],"award-info":[{"award-number":["61273008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["61273008"],"award-info":[{"award-number":["61273008"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"This paper is concerned withH<\/mml:mi>\u221e<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>control for linear positive discrete-time systems. Positive systems are characterized by nonnegative restriction on systems\u2019 variables. This restriction results in some remarkable results which are available only for linear positive systems. One of them is the celebrated diagonal positive definite matrix solutions to some existed well-known results for linear systems without nonnegative restriction. We provide an alternative proof for criterion ofH<\/mml:mi>\u221e<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>norm by using separating hyperplane theorem and Perron-Frobenius theorem for nonnegative matrices. We also considerH<\/mml:mi>\u221e<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>control problem for linear positive discrete-time systems via state feedback. Necessary and sufficient conditions for such problem are presented under controller gain with and without nonnegative restriction, and then the desired controller gains can be obtained from the feasible solutions.<\/jats:p>","DOI":"10.1155\/2013\/576379","type":"journal-article","created":{"date-parts":[[2013,9,11]],"date-time":"2013-09-11T17:01:46Z","timestamp":1378918906000},"page":"1-7","source":"Crossref","is-referenced-by-count":0,"title":["H<\/mml:mi>\u221e<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>Control for Linear Positive Discrete-Time Systems"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7012-9032","authenticated-orcid":true,"given":"Youmei","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Systems Science, Northeastern University, Shenyang 110819, China"},{"name":"Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingling","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamaki","family":"Tanaka","sequence":"additional","affiliation":[{"name":"Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/00207720701683033"},{"year":"2005","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1002\/9781118033029"},{"year":"2001","key":"4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019244121533"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(01)00146-3"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.1575"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2006.886888"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.900857"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.06.037"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2011.09.022"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2013.797106"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.02.023"},{"key":"16","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1002\/rnc.2836","volume":"23","year":"2013","journal-title":"International Journal of Robust and Nonlinear Control"},{"year":"2004","key":"17"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970777"},{"year":"1979","key":"19"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/576379.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/576379.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/576379.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T17:45:50Z","timestamp":1498067150000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/576379\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":17,"alternative-id":["576379","576379"],"URL":"https:\/\/doi.org\/10.1155\/2013\/576379","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}