{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T18:02:54Z","timestamp":1763748174206,"version":"3.40.3"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030509354"},{"type":"electronic","value":"9783030509361"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-50936-1_32","type":"book-chapter","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T05:03:00Z","timestamp":1592974980000},"page":"372-383","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Delay Product Type Lyapunov-Krasovskii Functional for Stability Analysis of Time-Delay System"],"prefix":"10.1007","author":[{"given":"Sharat Chandra","family":"Mahto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sandip","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shyam Krishna","family":"Nagar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pawel","family":"Dworak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,24]]},"reference":[{"issue":"7","key":"32_CR1","doi-asserted-by":"publisher","first-page":"1660","DOI":"10.1109\/TAC.2011.2121410","volume":"56","author":"C Briat","year":"2011","unstructured":"Briat, C.: Convergence and equivalence results for the jensen\u2019s inequality-application to time-delay and sampled-data systems. IEEE Trans. Autom. Control 56(7), 1660\u20131665 (2011)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"7","key":"32_CR2","doi-asserted-by":"publisher","first-page":"3488","DOI":"10.1109\/TAC.2016.2617739","volume":"62","author":"J Chen","year":"2016","unstructured":"Chen, J., Xu, S., Zhang, B.: Single\/multiple integral inequalities with applications to stability analysis of time-delay systems. IEEE Trans. Autom. Control 62(7), 3488\u20133493 (2016)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"10","key":"32_CR3","doi-asserted-by":"publisher","first-page":"54","DOI":"10.3182\/20060710-3-IT-4901.00010","volume":"39","author":"F Gouaisbaut","year":"2006","unstructured":"Gouaisbaut, F., Peaucelle, D.: Delay-dependent stability analysis of linear time delay systems. IFAC Proc. Vol. 39(10), 54\u201359 (2006)","journal-title":"IFAC Proc. Vol."},{"key":"32_CR4","doi-asserted-by":"crossref","unstructured":"Gu, K., Chen, J., Kharitonov, V.L.: Stability of Time-Delay Systems. Springer, Heidelberg (2003)","DOI":"10.1007\/978-1-4612-0039-0"},{"key":"32_CR5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.automatica.2015.08.025","volume":"64","author":"JH Kim","year":"2016","unstructured":"Kim, J.H.: Further improvement of jensen inequality and application to stability of time-delayed systems. Automatica 64, 121\u2013125 (2016)","journal-title":"Automatica"},{"issue":"12","key":"32_CR6","doi-asserted-by":"publisher","first-page":"5386","DOI":"10.1016\/j.jfranklin.2014.09.021","volume":"351","author":"O Kwon","year":"2014","unstructured":"Kwon, O., Park, M., Park, J.H., Lee, S., Cha, E.: Improved results on stability of linear systems with time-varying delays via wirtinger-based integral inequality. J. Franklin Inst. 351(12), 5386\u20135398 (2014)","journal-title":"J. Franklin Inst."},{"issue":"3","key":"32_CR7","doi-asserted-by":"publisher","first-page":"1176","DOI":"10.1016\/j.jfranklin.2017.12.014","volume":"355","author":"TH Lee","year":"2018","unstructured":"Lee, T.H., Park, J.H.: Improved stability conditions of time-varying delay systems based on new lyapunov functionals. J. Franklin Inst. 355(3), 1176\u20131191 (2018)","journal-title":"J. Franklin Inst."},{"key":"32_CR8","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.automatica.2016.08.011","volume":"75","author":"TH Lee","year":"2017","unstructured":"Lee, T.H., Park, J.H., Xu, S.: Relaxed conditions for stability of time-varying delay systems. Automatica 75, 11\u201315 (2017)","journal-title":"Automatica"},{"key":"32_CR9","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1016\/j.automatica.2018.03.073","volume":"93","author":"WI Lee","year":"2018","unstructured":"Lee, W.I., Lee, S.Y., Park, P.: Affine bessel-legendre inequality: application to stability analysis for systems with time-varying delays. Automatica 93, 535\u2013539 (2018)","journal-title":"Automatica"},{"key":"32_CR10","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.automatica.2016.11.001","volume":"76","author":"K Liu","year":"2017","unstructured":"Liu, K., Seuret, A., Xia, Y.: Stability analysis of systems with time-varying delays via the second-order bessel-legendre inequality. Automatica 76, 138\u2013142 (2017)","journal-title":"Automatica"},{"key":"32_CR11","doi-asserted-by":"crossref","unstructured":"Long, F., Zhang, C.K., Jiang, L., He, Y., Wu, M.: Stability analysis of systems with time-varying delay via improved lyapunov-krasovskii functionals. IEEE Trans. Syst. Man Cybern. Syst. (2019)","DOI":"10.1109\/TSMC.2019.2914367"},{"issue":"4","key":"32_CR12","doi-asserted-by":"publisher","first-page":"1378","DOI":"10.1016\/j.jfranklin.2015.01.004","volume":"352","author":"P Park","year":"2015","unstructured":"Park, P., Lee, W.I., Lee, S.Y.: Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. J. Franklin Inst. 352(4), 1378\u20131396 (2015)","journal-title":"J. Franklin Inst."},{"issue":"9","key":"32_CR13","doi-asserted-by":"publisher","first-page":"2860","DOI":"10.1016\/j.automatica.2013.05.030","volume":"49","author":"A Seuret","year":"2013","unstructured":"Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9), 2860\u20132866 (2013)","journal-title":"Automatica"},{"key":"32_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.sysconle.2015.03.007","volume":"81","author":"A Seuret","year":"2015","unstructured":"Seuret, A., Gouaisbaut, F.: Hierarchy of lmi conditions for the stability analysis of time-delay systems. Syst. Control Lett. 81, 1\u20137 (2015)","journal-title":"Syst. Control Lett."},{"key":"32_CR15","doi-asserted-by":"crossref","unstructured":"Seuret, A., Gouaisbaut, F.: Stability of linear systems with time-varying delays using bessel-legendre inequalities. IEEE Trans. Autom. Control (2017)","DOI":"10.1109\/TAC.2017.2730485"},{"issue":"2","key":"32_CR16","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1016\/j.automatica.2009.11.002","volume":"46","author":"J Sun","year":"2010","unstructured":"Sun, J., Liu, G., Chen, J., Rees, D.: Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2), 466\u2013470 (2010)","journal-title":"Automatica"},{"key":"32_CR17","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1016\/j.apm.2017.01.032","volume":"45","author":"HT Xu","year":"2017","unstructured":"Xu, H.T., Zhang, C.K., Jiang, L., Smith, J.: Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional. Appl. Math. Model. 45, 955\u2013964 (2017)","journal-title":"Appl. Math. Model."},{"issue":"3","key":"32_CR18","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1109\/TAC.2005.843873","volume":"50","author":"S Xu","year":"2005","unstructured":"Xu, S., Lam, J.: Improved delay-dependent stability criteria for time-delay systems. IEEE Trans. Autom. Control 50(3), 384\u2013387 (2005)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"10","key":"32_CR19","doi-asserted-by":"publisher","first-page":"2768","DOI":"10.1109\/TAC.2015.2404271","volume":"60","author":"HB Zeng","year":"2015","unstructured":"Zeng, H.B., He, Y., Wu, M., She, J.: Free-matrix-based integral inequality for stability analysis of systems with time-varying delay. IEEE Trans. Autom. Control 60(10), 2768\u20132772 (2015)","journal-title":"IEEE Trans. Autom. Control"},{"key":"32_CR20","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.automatica.2015.07.017","volume":"60","author":"HB Zeng","year":"2015","unstructured":"Zeng, H.B., He, Y., Wu, M., She, J.: New results on stability analysis for systems with discrete distributed delay. Automatica 60, 189\u2013192 (2015)","journal-title":"Automatica"},{"issue":"10","key":"32_CR21","doi-asserted-by":"publisher","first-page":"5331","DOI":"10.1109\/TAC.2016.2635381","volume":"62","author":"CK Zhang","year":"2017","unstructured":"Zhang, C.K., He, Y., Jiang, L., Wu, M.: Notes on stability of time-delay systems: bounding inequalities and augmented lyapunov-krasovskii functionals. IEEE Trans. Autom. Control 62(10), 5331\u20135336 (2017)","journal-title":"IEEE Trans. Autom. Control"},{"key":"32_CR22","unstructured":"Zhang, X.M., Han, Q.L., Ge, X., Zhang, B.L.: Passivity analysis of delayed neural networks based on Lyapunov-Krasovskii functionals with delay-dependent matrices. IEEE Trans. Cybern., 1\u201311 (2018)"},{"key":"32_CR23","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.automatica.2017.04.048","volume":"84","author":"XM Zhang","year":"2017","unstructured":"Zhang, X.M., Han, Q.L., Seuret, A., Gouaisbaut, F.: An improved reciprocally convex inequality and an augmented lyapunov-krasovskii functional for stability of linear systems with time-varying delay. Automatica 84, 221\u2013226 (2017)","journal-title":"Automatica"},{"issue":"1","key":"32_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1049\/iet-cta.2018.5188","volume":"13","author":"XM Zhang","year":"2018","unstructured":"Zhang, X.M., Han, Q.L., Seuret, A., Gouaisbaut, F., He, Y.: Overview of recent advances in stability of linear systems with time-varying delays. IET Control Theory Appl. 13(1), 1\u201316 (2018)","journal-title":"IET Control Theory Appl."},{"issue":"11","key":"32_CR25","doi-asserted-by":"publisher","first-page":"5319","DOI":"10.1109\/TNNLS.2018.2797279","volume":"29","author":"XM Zhang","year":"2018","unstructured":"Zhang, X.M., Han, Q.L., Wang, J.: Admissible delay upper bounds for global asymptotic stability of neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 29(11), 5319\u20135329 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."}],"container-title":["Advances in Intelligent Systems and Computing","Advanced, Contemporary Control"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-50936-1_32","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,10]],"date-time":"2020-10-10T04:09:05Z","timestamp":1602302945000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-50936-1_32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030509354","9783030509361"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-50936-1_32","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"24 June 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}