{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T17:23:25Z","timestamp":1706030605921},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T00:00:00Z","timestamp":1679011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Postdoctoral Scholarship Programme of Vingroup Innovation Foundation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,6,16]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, for the first time, a linear Lyapunov\u2013Razumikhin function is introduced to find an $\\alpha$-exponential state estimate for positive systems with time delays. A new set of conditions for the existence of exponential state boundedness of positive systems with bounded time-varying delays is established. Two procedures are then proposed to find the factor vector of $\\alpha$-exponential state estimate, in which some techniques of optimization are applied to find the smallest possible factor vector. Numerical experiments are presented to demonstrate the effectiveness of the linear Lyapunov\u2013Razumikhin function as well as of the optimization techniques.<\/jats:p>","DOI":"10.1093\/imamci\/dnad003","type":"journal-article","created":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T17:36:27Z","timestamp":1679074587000},"page":"135-151","source":"Crossref","is-referenced-by-count":1,"title":["Exponential state estimate of positive systems with time-varying delays: a Lyapunov\u2013Razumikhin approach"],"prefix":"10.1093","volume":"40","author":[{"given":"Tran","family":"Ngoc Nguyen","sequence":"first","affiliation":[{"name":"Quy Nhon University Department of Mathematics and Statistics, , Quy Nhon, Binh Dinh, Vietnam"}]}],"member":"286","published-online":{"date-parts":[[2023,3,17]]},"reference":[{"key":"2023061612573454600_ref1","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/978-3-642-02894-6_20","article-title":"Stability analysis and synthesis for linear positive systems with time-varying delays","volume-title":"Positive Systems","author":"Ait Rami","year":"2009"},{"key":"2023061612573454600_ref2","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.ejcon.2013.05.001","article-title":"Estimation of linear positive systems with unknown time-varying delays","volume":"19","author":"Ait Rami","year":"2013","journal-title":"Eur. 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