{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:33:33Z","timestamp":1760402013963,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,2]],"date-time":"2020-05-02T00:00:00Z","timestamp":1588377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this manuscript, we consider the finite-time     H \u221e     control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a     H \u221e     controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time     H \u221e     state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.<\/jats:p>","DOI":"10.3390\/sym12050713","type":"journal-article","created":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T06:41:20Z","timestamp":1588660880000},"page":"713","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Time-Varying Delayed H\u221e Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach"],"prefix":"10.3390","volume":"12","author":[{"given":"Chanikan","family":"Emharuethai","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Maejo University, Chiangmai 50290, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piyapong","family":"Niamsup","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Chiangmai University, Chiangmai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0830-4933","authenticated-orcid":false,"given":"Raja","family":"Ramachandran","sequence":"additional","affiliation":[{"name":"Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wajaree","family":"Weera","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Pha Yao, Pha Yao 56000, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1016\/j.jfranklin.2015.01.004","article-title":"Auxiliary function-based integral inequalities for quadratic functions and there applications to time delay systems","volume":"352","author":"Park","year":"2015","journal-title":"J. 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