{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T21:35:25Z","timestamp":1777498525101,"version":"3.51.4"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s11432-024-4220-6","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T08:53:16Z","timestamp":1743756796000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A discrete-time looped functional approach and its application to discrete-time systems with cyclically varying delays"],"prefix":"10.1007","volume":"68","author":[{"given":"Wen-Hu","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuan-Ke","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen-Rui","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke-You","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong-Bing","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"4220_CR1","doi-asserted-by":"publisher","first-page":"122202","DOI":"10.1007\/s11432-021-3433-8","volume":"66","author":"J He","year":"2023","unstructured":"He J, Liang Y, Hao X, et al. A quadratic convex framework with bigger freedom for the stability analysis of a cyber-physical microgrid system. Sci China Inf Sci, 2023, 66: 122202","journal-title":"Sci China Inf Sci"},{"key":"4220_CR2","doi-asserted-by":"publisher","first-page":"6099","DOI":"10.1016\/j.jfranklin.2023.04.019","volume":"360","author":"W Wang","year":"2023","unstructured":"Wang W, Zeng H B, Teo K L, et al. Relaxed stability criteria of time-varying delay systems via delay-derivative-dependent slack matrices. J Franklin Inst, 2023, 360: 6099\u20136109","journal-title":"J Franklin Inst"},{"key":"4220_CR3","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1109\/TFUZZ.2022.3204899","volume":"31","author":"T S Peng","year":"2023","unstructured":"Peng T S, Zeng H B, Wang W, et al. General and less conservative criteria on stability and stabilization of T-S fuzzy systems with time-varying delay. IEEE Trans Fuzzy Syst, 2023, 31: 1531\u20131541","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4220_CR4","doi-asserted-by":"publisher","first-page":"6101","DOI":"10.1109\/TFUZZ.2024.3440264","volume":"32","author":"W H Chen","year":"2024","unstructured":"Chen W H, Zhang C K, Liu Z Z, et al. Stability and filtering for delayed discrete-time T-S fuzzy systems via membership-dependent approaches. IEEE Trans Fuzzy Syst, 2024, 32: 6101\u20136111","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4220_CR5","doi-asserted-by":"publisher","first-page":"2582","DOI":"10.1109\/TAC.2016.2600024","volume":"62","author":"C K Zhang","year":"2017","unstructured":"Zhang C K, He Y, Jiang L, et al. Summation inequalities to bounded real lemmas of discrete-time systems with time-varying delay. IEEE Trans Automat Contr, 2017, 62: 2582\u20132588","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR6","doi-asserted-by":"publisher","first-page":"951","DOI":"10.1049\/cth2.12632","volume":"18","author":"H Sha","year":"2024","unstructured":"Sha H, Park J H, Chen J, et al. Stability analysis of discrete-time systems with a time-varying delay via improved methods. IET Control Theor Appl, 2024, 18: 951\u2013959","journal-title":"IET Control Theor Appl"},{"key":"4220_CR7","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1109\/TAC.2006.890320","volume":"52","author":"H Gao","year":"2007","unstructured":"Gao H, Chen T. New results on stability of discrete-time systems with time-varying state delay. IEEE Trans Automat Contr, 2007, 52: 328\u2013334","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR8","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/j.jfranklin.2012.12.013","volume":"350","author":"O M Kwon","year":"2013","unstructured":"Kwon O M, Park M J, Park J H, et al. Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional. J Franklin Inst, 2013, 350: 521\u2013540","journal-title":"J Franklin Inst"},{"key":"4220_CR9","doi-asserted-by":"publisher","first-page":"4779","DOI":"10.1002\/rnc.5009","volume":"30","author":"J Chen","year":"2020","unstructured":"Chen J, Park J H, Xu S, et al. Stability of discrete-time systems with time-varying delay via a novel Lyapunov-Krasovskii functional. Intl J Robust Nonlinear, 2020, 30: 4779\u20134788","journal-title":"Intl J Robust Nonlinear"},{"key":"4220_CR10","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1016\/j.automatica.2009.12.004","volume":"46","author":"X Meng","year":"2010","unstructured":"Meng X, Lam J, Du B, et al. A delay-partitioning approach to the stability analysis of discrete-time systems. Automatica, 2010, 46: 610\u2013614","journal-title":"Automatica"},{"key":"4220_CR11","doi-asserted-by":"publisher","first-page":"2372","DOI":"10.1109\/TAC.2008.2007522","volume":"53","author":"Y He","year":"2008","unstructured":"He Y, Wu M, Liu G P, et al. Output feedback stabilization for a discrete-time system with a time-varying delay. IEEE Trans Automat Contr, 2008, 53: 2372\u20132377","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR12","first-page":"1644","volume-title":"Proceedings of American Control Conference","author":"X L Zhu","year":"2008","unstructured":"Zhu X L, Yang G H. Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay. In: Proceedings of American Control Conference, 2008. 1644\u20131649"},{"key":"4220_CR13","doi-asserted-by":"publisher","first-page":"2740","DOI":"10.1109\/TAC.2015.2398885","volume":"60","author":"A Seuret","year":"2015","unstructured":"Seuret A, Gouaisbaut F, Fridman E. Stability of discrete-time systems with time-varying delays via a novel summation inequality. IEEE Trans Automat Contr, 2015, 60: 2740\u20132745","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR14","doi-asserted-by":"publisher","first-page":"5810","DOI":"10.1016\/j.jfranklin.2015.09.018","volume":"352","author":"P T Nam","year":"2015","unstructured":"Nam P T, Trinh H, Pathirana P N. Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems. J Franklin Inst, 2015, 352: 5810\u20135831","journal-title":"J Franklin Inst"},{"key":"4220_CR15","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.automatica.2016.12.036","volume":"78","author":"X G Liu","year":"2017","unstructured":"Liu X G, Wang F X, Tang M L. Auxiliary function-based summation inequalities and their applications to discrete-time systems. Automatica, 2017, 78: 211\u2013215","journal-title":"Automatica"},{"key":"4220_CR16","doi-asserted-by":"publisher","first-page":"104543","DOI":"10.1016\/j.sysconle.2019.104543","volume":"134","author":"S B Qiu","year":"2019","unstructured":"Qiu S B, Liu X G, Wang F X, et al. Stability and passivity analysis of discrete-time linear systems with time-varying delay. Syst Control Lett, 2019, 134: 104543","journal-title":"Syst Control Lett"},{"key":"4220_CR17","first-page":"128025","volume":"451","author":"J M Park","year":"2023","unstructured":"Park J M, Kwon N K, Lee S Y. Extended affine bessel summation inequalities: applications to stability analysis of linear discrete-time systems with time-varying delays. Appl Math Comput, 2023, 451: 128025","journal-title":"Appl Math Comput"},{"key":"4220_CR18","doi-asserted-by":"publisher","first-page":"111192","DOI":"10.1016\/j.automatica.2023.111192","volume":"156","author":"C K Zhang","year":"2023","unstructured":"Zhang C K, Chen W H, Zhu C, et al. Stability analysis of discrete-time systems with time-varying delay via a delay-dependent matrix-separation-based inequality. Automatica, 2023, 156: 111192","journal-title":"Automatica"},{"key":"4220_CR19","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.automatica.2010.10.014","volume":"47","author":"P G Park","year":"2011","unstructured":"Park P G, Ko J W, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47: 235\u2013238","journal-title":"Automatica"},{"key":"4220_CR20","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1016\/j.automatica.2017.07.056","volume":"85","author":"C K Zhang","year":"2017","unstructured":"Zhang C K, He Y, Jiang L, et al. An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay. Automatica, 2017, 85: 481\u2013485","journal-title":"Automatica"},{"key":"4220_CR21","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1016\/j.automatica.2018.06.017","volume":"95","author":"A Seuret","year":"2018","unstructured":"Seuret A, Liu K, Gouaisbaut F. Generalized reciprocally convex combination lemmas and its application to time-delay systems. Automatica, 2018, 95: 488\u2013493","journal-title":"Automatica"},{"key":"4220_CR22","doi-asserted-by":"publisher","first-page":"9930","DOI":"10.1016\/j.jfranklin.2020.07.034","volume":"357","author":"H B Zeng","year":"2020","unstructured":"Zeng H B, Lin H C, He Y, et al. Hierarchical stability conditions for time-varying delay systems via an extended reciprocally convex quadratic inequality. J Franklin Inst, 2020, 357: 9930\u20139941","journal-title":"J Franklin Inst"},{"key":"4220_CR23","doi-asserted-by":"publisher","first-page":"7491","DOI":"10.1109\/TNNLS.2022.3144032","volume":"34","author":"H C Lin","year":"2023","unstructured":"Lin H C, Zeng H B, Zhang X M, et al. Stability analysis for delayed neural networks via a generalized reciprocally convex inequality. IEEE Trans Neural Netw Learn Syst, 2023, 34: 7491\u20137499","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4220_CR24","doi-asserted-by":"publisher","first-page":"108764","DOI":"10.1016\/j.automatica.2019.108764","volume":"113","author":"C K Zhang","year":"2020","unstructured":"Zhang C K, Long F, He Y, et al. A relaxed quadratic function negative-determination lemma and its application to time-delay systems. Automatica, 2020, 113: 108764","journal-title":"Automatica"},{"key":"4220_CR25","first-page":"124866","volume":"369","author":"F S S de Oliveira","year":"2020","unstructured":"de Oliveira F S S, Souza F O. Further refinements in stability conditions for time-varying delay systems. Appl Math Comput, 2020, 369: 124866","journal-title":"Appl Math Comput"},{"key":"4220_CR26","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1109\/JAS.2020.1003111","volume":"8","author":"X M Zhang","year":"2021","unstructured":"Zhang X M, Han Q L, Ge X. Novel stability criteria for linear time-delay systems using Lyapunov-Krasovskii functionals with a cubic polynomial on time-varying delay. IEEE CAA J Autom Sin, 2021, 8: 77\u201385","journal-title":"IEEE CAA J Autom Sin"},{"key":"4220_CR27","doi-asserted-by":"publisher","first-page":"159201","DOI":"10.1007\/s11432-020-3221-6","volume":"66","author":"C K Zhang","year":"2023","unstructured":"Zhang C K, Xie K Y, He Y, et al. Matrix-injection-based transformation method for discrete-time systems with time-varying delay. Sci China Inf Sci, 2023, 66: 159201","journal-title":"Sci China Inf Sci"},{"key":"4220_CR28","doi-asserted-by":"publisher","first-page":"110010","DOI":"10.1016\/j.automatica.2021.110010","volume":"136","author":"X M Zhang","year":"2022","unstructured":"Zhang X M, Han Q L, Ge X. A novel approach to H\u221e performance analysis of discrete-time networked systems subject to network-induced delays and malicious packet dropouts. Automatica, 2022, 136: 110010","journal-title":"Automatica"},{"key":"4220_CR29","doi-asserted-by":"publisher","first-page":"2663","DOI":"10.1109\/TAC.2015.2503047","volume":"61","author":"C K Zhang","year":"2016","unstructured":"Zhang C K, He Y, Jiang L, et al. Delay-variation-dependent stability of delayed discrete-time systems. IEEE Trans Automat Contr, 2016, 61: 2663\u20132669","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR30","doi-asserted-by":"publisher","first-page":"6951","DOI":"10.1016\/j.jfranklin.2020.04.052","volume":"357","author":"P T Nam","year":"2020","unstructured":"Nam P T, Luu T H. A new delay-variation-dependent stability criterion for delayed discrete-time systems. J Franklin Inst, 2020, 357: 6951\u20136967","journal-title":"J Franklin Inst"},{"key":"4220_CR31","doi-asserted-by":"publisher","first-page":"4976","DOI":"10.1016\/j.jfranklin.2022.04.023","volume":"359","author":"X Ge","year":"2022","unstructured":"Ge X, Hoi K, Vong S. A delay-variation-dependent stability criterion for discrete-time systems via a bivariate quadratic function negative-determination lemma. J Franklin Inst, 2022, 359: 4976\u20134996","journal-title":"J Franklin Inst"},{"key":"4220_CR32","doi-asserted-by":"publisher","first-page":"110592","DOI":"10.1016\/j.automatica.2022.110592","volume":"147","author":"X M Zhang","year":"2023","unstructured":"Zhang X M, Han Q L, Ge X, et al. Stability analysis of delayed discrete-time systems based on a delay-square-dependent Lyapunov functional. Automatica, 2023, 147: 110592","journal-title":"Automatica"},{"key":"4220_CR33","doi-asserted-by":"publisher","first-page":"1578","DOI":"10.1109\/TNNLS.2021.3105591","volume":"34","author":"X M Zhang","year":"2023","unstructured":"Zhang X M, Han Q L, Ge X, et al. Delay-variation-dependent criteria on extended dissipativity for discrete-time neural networks with time-varying delay. IEEE Trans Neural Netw Learn Syst, 2023, 34: 1578\u20131587","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4220_CR34","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1109\/TAC.2017.2730485","volume":"63","author":"A Seuret","year":"2018","unstructured":"Seuret A, Gouaisbaut F. Stability of linear systems with time-varying delays using Bessel-Legendre inequalities. IEEE Trans Automat Contr, 2018, 63: 225\u2013232","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR35","doi-asserted-by":"publisher","first-page":"105721","DOI":"10.1016\/j.sysconle.2024.105721","volume":"184","author":"C R Wang","year":"2024","unstructured":"Wang C R, He Y, Zhang C K, et al. Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay. Syst Control Lett, 2024, 184: 105721","journal-title":"Syst Control Lett"},{"key":"4220_CR36","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.automatica.2011.09.033","volume":"48","author":"A Seuret","year":"2012","unstructured":"Seuret A. A novel stability analysis of linear systems under asynchronous samplings. Automatica, 2012, 48: 177\u2013182","journal-title":"Automatica"},{"key":"4220_CR37","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/j.automatica.2017.04.051","volume":"82","author":"H B Zeng","year":"2017","unstructured":"Zeng H B, Teo K L, He Y. A new looped-functional for stability analysis of sampled-data systems. Automatica, 2017, 82: 328\u2013331","journal-title":"Automatica"},{"key":"4220_CR38","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.arcontrol.2023.03.004","volume":"55","author":"X M Zhang","year":"2023","unstructured":"Zhang X M, Han Q L, Ge X, et al. Sampled-data control systems with non-uniform sampling: a survey of methods and trends. Annu Rev Control, 2023, 55: 70\u201391","journal-title":"Annu Rev Control"},{"key":"4220_CR39","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1109\/TAC.2005.844723","volume":"50","author":"W Michiels","year":"2005","unstructured":"Michiels W, van Assche V, Niculescu S I. Stabilization of time-delay systems with a controlled time-varying delay and applications. IEEE Trans Automat Contr, 2005, 50: 493\u2013504","journal-title":"IEEE Trans Automat Contr"},{"key":"4220_CR40","doi-asserted-by":"publisher","first-page":"110030","DOI":"10.1016\/j.automatica.2021.110030","volume":"138","author":"H B Zeng","year":"2022","unstructured":"Zeng H B, He Y, Teo K L. Monotone-delay-interval-based Lyapunov functionals for stability analysis of systems with a periodically varying delay. Automatica, 2022, 138: 110030","journal-title":"Automatica"},{"key":"4220_CR41","doi-asserted-by":"publisher","first-page":"149202","DOI":"10.1007\/s11432-020-3201-7","volume":"66","author":"H B Zeng","year":"2023","unstructured":"Zeng H B, Lin H C, He Y, et al. Stability analysis of a class of systems with periodically varying delay via looped-functional-based Lyapunov functional. Sci China Inf Sci, 2023, 66: 149202","journal-title":"Sci China Inf Sci"},{"key":"4220_CR42","doi-asserted-by":"publisher","first-page":"980","DOI":"10.1016\/j.sysconle.2012.07.008","volume":"61","author":"C Briat","year":"2012","unstructured":"Briat C, Seuret A. A looped-functional approach for robust stability analysis of linear impulsive systems. Syst Control Lett, 2012, 61: 980\u2013988","journal-title":"Syst Control Lett"},{"key":"4220_CR43","doi-asserted-by":"publisher","first-page":"4856","DOI":"10.1109\/TFUZZ.2022.3162104","volume":"30","author":"W H Chen","year":"2022","unstructured":"Chen W H, Zhang C K, Xie K Y, et al. Delay-variation-dependent criteria on stability and stabilization for discrete-time T-S fuzzy systems with time-varying delays. IEEE Trans Fuzzy Syst, 2022, 30: 4856\u20134866","journal-title":"IEEE Trans Fuzzy Syst"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-024-4220-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11432-024-4220-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-024-4220-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T01:27:57Z","timestamp":1743816477000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11432-024-4220-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":43,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["4220"],"URL":"https:\/\/doi.org\/10.1007\/s11432-024-4220-6","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"value":"1674-733X","type":"print"},{"value":"1869-1919","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,25]]},"assertion":[{"value":"3 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"182204"}}