{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:16:32Z","timestamp":1760242592316,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,12,3]],"date-time":"2017-12-03T00:00:00Z","timestamp":1512259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chinese Ministry of Education","award":["2014XS46"],"award-info":[{"award-number":["2014XS46"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A novel stability analysis for the interval time-delay systems is proposed by employing a new series of integral inequalities for single and double integrals. Different from the recently introduced Wirtinger-based inequalities, refined Jensen inequalities and auxiliary function-based inequalities, the proposed ones can provide more accurate bounds for the cross terms in derivatives of the Lyapunov\u2013Krasovskii functional (LKF) without involving additional slack variables. Based on the augmented LKF with triple-integral terms, their applications to stability analysis for interval time-delay systems are provided. By virtue of the newly derived inequalities, the resulting criteria are less conservative than some existing literature. Finally, numerical examples are provided to verify the effectiveness and improvement of the proposed approaches.<\/jats:p>","DOI":"10.3390\/a10040134","type":"journal-article","created":{"date-parts":[[2017,12,4]],"date-time":"2017-12-04T11:16:38Z","timestamp":1512386198000},"page":"134","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3029-9619","authenticated-orcid":false,"given":"Shuai","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China"}]},{"given":"Xiao","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1016\/j.automatica.2014.03.017","article-title":"A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems","volume":"50","author":"Guo","year":"2014","journal-title":"Automatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2281","DOI":"10.1016\/j.automatica.2013.04.021","article-title":"Network-based leader-following consensus for distributed multi-agent systems","volume":"49","author":"Ding","year":"2013","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1109\/TFUZZ.2011.2174244","article-title":"Reliable fuzzy control for active suspension systems with actuator delay and fault","volume":"20","author":"Li","year":"2012","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1109\/TCST.2009.2015653","article-title":"Robust sampled-data control for vehicle active suspension systems","volume":"18","author":"Gao","year":"2010","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1109\/TAC.2010.2095591","article-title":"New stability criteria for linear discrete-time systems with interval-like time-varying delays","volume":"56","author":"Shao","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.automatica.2015.11.010","article-title":"Mode-identifying time estimation and switching-delay tolerant control for switched systems: An elementary time unit approach","volume":"64","author":"Zhang","year":"2016","journal-title":"Automatica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.automatica.2016.04.048","article-title":"Razumikhin and Krasovskii stability theorems for time-varying time-delay systems","volume":"71","author":"Zhou","year":"2016","journal-title":"Automatica"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.3390\/a8010003","article-title":"Networked control system time-delay compensation based on time-delay prediction and improved implicit GPC","volume":"8","author":"Tian","year":"2015","journal-title":"Algorithms"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"743","DOI":"10.3390\/a8030743","article-title":"A CS recovery algorithm for model and time delay identification of MISO-FIR systems","volume":"8","author":"Liu","year":"2015","journal-title":"Algorithms"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.isatra.2017.01.030","article-title":"Further results on stabilization for interval time-delay systems via new integral inequality approach","volume":"68","author":"Li","year":"2017","journal-title":"ISA Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4892","DOI":"10.1016\/j.jfranklin.2014.07.015","article-title":"Stability analysis for interval time-varying delay systems based on time-varying bound integral method","volume":"351","author":"Qian","year":"2014","journal-title":"J. Franklin Inst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1109\/TNNLS.2013.2285564","article-title":"New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach","volume":"25","author":"Ge","year":"2014","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.isatra.2013.11.020","article-title":"A novel approach to delay-fractional-dependent stability criterion for linear systems with interval delay","volume":"53","author":"An","year":"2014","journal-title":"ISA Trans."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.automatica.2009.11.002","article-title":"Improved delay-range-dependent stability criteria for linear systems with time-varying delays","volume":"46","author":"Sun","year":"2010","journal-title":"Automatica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1002\/rnc.3106","article-title":"Optimal partitioning method for stability analysis of continuous\/discrete delay systems","volume":"25","author":"Feng","year":"2015","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2118","DOI":"10.1016\/j.automatica.2011.05.023","article-title":"Note on stability of linear systems with time-varying delay","volume":"47","author":"Kim","year":"2011","journal-title":"Automatica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4407","DOI":"10.1016\/j.jfranklin.2015.06.023","article-title":"An enhanced stability criterion for time-delay systems via a new bounding technique","volume":"352","author":"Hien","year":"2015","journal-title":"J. Franklin Inst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1109\/TAC.2011.2121410","article-title":"Convergence and equivalence results for the Jensen\u2019s inequality-application to time-delay and sample-data systems","volume":"57","author":"Briat","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2860","DOI":"10.1016\/j.automatica.2013.05.030","article-title":"Wirtinger-based integral inequality: Application to time-delay systems","volume":"49","author":"Seuret","year":"2013","journal-title":"Automatica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.automatica.2015.07.017","article-title":"New results on stability analysis for systems with discrete distributed delay","volume":"60","author":"Zeng","year":"2015","journal-title":"Automatica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.sysconle.2016.03.002","article-title":"Stability analysis of systems with time-varying delay via relaxed integral inequalities","volume":"92","author":"Zhang","year":"2016","journal-title":"Syst. Control Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.automatica.2015.03.010","article-title":"Stability of time-delay systems via Wirtinger-based double integral inequality","volume":"55","author":"Park","year":"2015","journal-title":"Automatica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2188","DOI":"10.1049\/iet-cta.2014.0962","article-title":"Refined Jensen-based inequality approach to stability analysis of time-delay systems","volume":"9","author":"Hien","year":"2015","journal-title":"IET Control Theory Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1016\/j.jfranklin.2016.11.015","article-title":"Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances","volume":"354","author":"Mohajerpoor","year":"2017","journal-title":"J. Franklin Inst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mohajerpoor, R., Shanmugam, L., Abdi, H., Rakkiyappan, R., Nahavandi, S., and Shi, P. (2017). New delay range-dependent stability criteria for interval time-varying delay systems via Wirtinger-based inequalities. Int. J. Robust Nonlinear Control.","DOI":"10.1002\/rnc.3893"},{"key":"ref_26","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 their applications to time-delay systems","volume":"352","author":"Park","year":"2015","journal-title":"J. Franklin Inst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.automatica.2010.10.014","article-title":"Reciprocally convex approach to stability of systems with time-varying delays","volume":"47","author":"Park","year":"2011","journal-title":"Automatica"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.amc.2013.06.028","article-title":"Stability analysis of static recurrent neural networks with interval time-varying delay","volume":"221","author":"Sun","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1486","DOI":"10.1109\/TNNLS.2015.2449898","article-title":"Stability analysis for delayed neural networks considering both conservativeness and complexity","volume":"27","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1016\/j.automatica.2008.09.010","article-title":"New delay-dependent stability criteria for systems with interval delay","volume":"45","author":"Shao","year":"2009","journal-title":"Automatica"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2680","DOI":"10.1016\/j.automatica.2008.02.020","article-title":"New stability criteria for linear systems with interval time-varying delay","volume":"44","author":"Jiang","year":"2008","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.1016\/j.automatica.2009.08.002","article-title":"New conditions for delay-derivative dependent stability","volume":"45","author":"Fridman","year":"2009","journal-title":"Automatica"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.isatra.2013.10.004","article-title":"Further results on delay-range-dependent stability with additive time-varying delay systems","volume":"53","author":"Liu","year":"2014","journal-title":"ISA Trans."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1049\/iet-cta.2009.0176","article-title":"New stability criteria for continuous-time systems with interval time-varying delay","volume":"4","author":"Zhu","year":"2010","journal-title":"IET Control Theory Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1049\/iet-cta.2011.0360","article-title":"Improved delay-range-dependent stability criteria for linear systems with interval time-varying delays","volume":"6","author":"Tang","year":"2012","journal-title":"IET Control Theory Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2768","DOI":"10.1109\/TAC.2015.2404271","article-title":"Free-matrix-based integral inequality for stability analysis of systems with time-varying delay","volume":"60","author":"Zeng","year":"2015","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.automatica.2006.08.015","article-title":"Delay-range-dependent stability for systems with time-varying delay","volume":"43","author":"He","year":"2007","journal-title":"Automatica"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/4\/134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:52:25Z","timestamp":1760208745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/4\/134"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,3]]},"references-count":37,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["a10040134"],"URL":"https:\/\/doi.org\/10.3390\/a10040134","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2017,12,3]]}}}