{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T14:55:23Z","timestamp":1779116123150,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T00:00:00Z","timestamp":1670284800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T00:00:00Z","timestamp":1670284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"crossref","award":["62073011"],"award-info":[{"award-number":["62073011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"crossref","award":["61973135"],"award-info":[{"award-number":["61973135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021MF004"],"award-info":[{"award-number":["ZR2021MF004"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s40815-022-01409-6","type":"journal-article","created":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T05:02:35Z","timestamp":1670302955000},"page":"851-867","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Robust Non-fragile $$H_{\\infty }$$ Fuzzy Control for Uncertain Nonlinear-Delayed Hyperbolic PDE Systems"],"prefix":"10.1007","volume":"25","author":[{"given":"Xu","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6269-789X","authenticated-orcid":false,"given":"Zi-Peng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huai-Ning","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Wei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han-Xiong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun-Fei","family":"Qiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,12,6]]},"reference":[{"key":"1409_CR1","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1007\/s40815-021-01189-5","volume":"24","author":"M Liang","year":"2022","unstructured":"Liang, M., Chang, Y., Zhang, F., Wang, S., Wang, C., Lu, S., Wang, Y.: Observer-based adaptive fuzzy output feedback control for a class of fractional-order nonlinear systems with full-state constraints. Int. J. Fuzzy Syst. 24, 1046\u20131058 (2022)","journal-title":"Int. J. Fuzzy Syst."},{"key":"1409_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-022-01304-0","author":"X Song","year":"2022","unstructured":"Song, X., Sun, P., Song, S., Wu, Q., Lu, J.: Event-triggered fuzzy adaptive fixed-time output-feedback control for nonlinear systems with multiple objective constraints. Int. J. Fuzzy Syst. (2022). https:\/\/doi.org\/10.1007\/s40815-022-01304-0","journal-title":"Int. J. Fuzzy Syst."},{"issue":"1","key":"1409_CR3","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1109\/TSMC.1985.6313399","volume":"15","author":"T Takagi","year":"1985","unstructured":"Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116\u2013132 (1985)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"1409_CR4","doi-asserted-by":"publisher","DOI":"10.1002\/0471224596","volume-title":"Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach","author":"K Tanaka","year":"2001","unstructured":"Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2001)"},{"key":"1409_CR5","volume-title":"Analysis and Synthesis of Fuzzy Control Systems: A Model Based Approach","author":"G Feng","year":"2010","unstructured":"Feng, G.: Analysis and Synthesis of Fuzzy Control Systems: A Model Based Approach. CRC Press, Boca Raton (2010)"},{"key":"1409_CR6","volume-title":"Advanced Process Control","author":"W-H Ray","year":"1981","unstructured":"Ray, W.-H.: Advanced Process Control. McGraw-Hill, New York (1981)"},{"key":"1409_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4224-6","volume-title":"An Introduction to Infinite-Dimensional Linear Systems Theory","author":"RF Curtain","year":"1995","unstructured":"Curtain, R.F., Zwart, H.: An Introduction to Infinite-Dimensional Linear Systems Theory. Springer, New York (1995)"},{"issue":"1","key":"1409_CR8","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.arcontrol.2009.01.003","volume":"33","author":"R Padhi","year":"2009","unstructured":"Padhi, R., Ali, S.F.: An account of chronological developments in control of distributed parameter systems. Annu. Rev. Control. 33(1), 59\u201368 (2009)","journal-title":"Annu. Rev. Control."},{"issue":"3","key":"1409_CR9","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1109\/TFUZZ.2011.2116028","volume":"19","author":"J-W Wang","year":"2011","unstructured":"Wang, J.-W., Wu, H.-N., Li, H.-X.: Distributed fuzzy control design of nonlinear hyperbolic PDE systems with application to nonisothermal plug-flow reactor. IEEE Trans. Fuzzy Syst. 19(3), 514\u2013526 (2011)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1409_CR10","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.fss.2014.03.007","volume":"254","author":"J-W Wang","year":"2014","unstructured":"Wang, J.-W., Wu, H.-N.: Fuzzy output tracking control of semi-linear first-order hyperbolic PDE systems with matched perturbations. Fuzzy Sets Syst. 254, 47\u201366 (2014)","journal-title":"Fuzzy Sets Syst."},{"issue":"2","key":"1409_CR11","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1109\/TFUZZ.2015.2457934","volume":"24","author":"J Qiu","year":"2016","unstructured":"Qiu, J., Ding, S.-X., Gao, H., Yin, S.: Fuzzy-model-based reliable static output feedback $$H_{\\infty }$$ control of nonlinear hyperbolic PDE systems. IEEE Trans. Fuzzy Syst. 24(2), 388\u2013400 (2016)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"9","key":"1409_CR12","doi-asserted-by":"publisher","first-page":"2060","DOI":"10.1016\/j.automatica.2009.04.026","volume":"45","author":"E Fridman","year":"2009","unstructured":"Fridman, E., Orlov, Y.: An LMI approach to $$H_{\\infty }$$ boundary control of semilinear parabolic and hyperbolic systems. Automatica 45(9), 2060\u20132066 (2009)","journal-title":"Automatica"},{"issue":"10","key":"1409_CR13","doi-asserted-by":"publisher","first-page":"2535","DOI":"10.1016\/j.automatica.2012.06.043","volume":"48","author":"H-N Wu","year":"2012","unstructured":"Wu, H.-N., Wang, J.-W., Li, H.-X.: Design of distributed $$H_{\\infty }$$ fuzzy controllers with constraint for nonlinear hyperbolic PDE systems. Automatica 48(10), 2535\u20132543 (2012)","journal-title":"Automatica"},{"issue":"7","key":"1409_CR14","doi-asserted-by":"publisher","first-page":"3789","DOI":"10.1109\/TCYB.2019.2942685","volume":"51","author":"S-H Tsai","year":"2021","unstructured":"Tsai, S.-H., Wang, J.-W., Song, E.-S., Lam, H.-K.: Robust $$H_{\\infty }$$ control for nonlinear hyperbolic PDE systems based on the polynomial fuzzy model. IEEE Trans. Cybern. 51(7), 3789\u20133801 (2021)","journal-title":"IEEE Trans. Cybern."},{"issue":"2","key":"1409_CR15","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1109\/TAC.2006.887907","volume":"52","author":"Y He","year":"2007","unstructured":"He, Y., Wang, Q.-G., Xie, L.H., Lin, C.: Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control 52(2), 293\u2013299 (2007)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"9","key":"1409_CR16","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"},{"issue":"1","key":"1409_CR17","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.automatica.2008.06.006","volume":"45","author":"E Fridman","year":"2009","unstructured":"Fridman, E., Orlov, Y.: Exponential stability of linear distributed parameter systems with time-varying delays. Automatica 45(1), 194\u2013201 (2009)","journal-title":"Automatica"},{"issue":"5","key":"1409_CR18","doi-asserted-by":"publisher","first-page":"051003","DOI":"10.1115\/1.4038374","volume":"140","author":"J-W Wang","year":"2018","unstructured":"Wang, J.-W., Sun, C.-Y.: Delay-dependent exponential stabilization for linear distributed parameter systems with time-varying delay. J. Dyn. Syst. Meas. Control 140(5), 051003 (2018)","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"1409_CR19","doi-asserted-by":"publisher","first-page":"108993","DOI":"10.1016\/j.automatica.2020.108993","volume":"117","author":"H-N Wu","year":"2020","unstructured":"Wu, H.-N., Zhang, X.-W.: Static output feedback stabilization for a linear parabolic PDE system with time-varying delay via mobile collocated actuator\/sensor pairs. Automatica 117, 108993 (2020)","journal-title":"Automatica"},{"issue":"3","key":"1409_CR20","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1109\/TFUZZ.2007.896233","volume":"16","author":"K Yuan","year":"2008","unstructured":"Yuan, K., Li, H.-X., Cao, J.: Robust stabilization of the distributed parameter system with time delay via fuzzy control. IEEE Trans. Fuzzy Syst. 16(3), 567\u2013584 (2008)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"6","key":"1409_CR21","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1109\/TFUZZ.2010.2058809","volume":"18","author":"Y-T Chang","year":"2010","unstructured":"Chang, Y.-T., Chen, B.-S.: A fuzzy approach for robust referencetracking-control design of nonlinear distributed parameter time-delayed systems and its application. IEEE Trans. Fuzzy Syst. 18(6), 1041\u20131057 (2010)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"10","key":"1409_CR22","doi-asserted-by":"publisher","first-page":"3054","DOI":"10.1109\/TFUZZ.2020.3012392","volume":"29","author":"Z-P Wang","year":"2021","unstructured":"Wang, Z.-P., Wu, H.-N., Huang, T.: Sampled-data fuzzy control for nonlinear delayed distributed parameter systems. IEEE Trans. Fuzzy Syst. 29(10), 3054\u20133066 (2021)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"5","key":"1409_CR23","doi-asserted-by":"publisher","first-page":"3947","DOI":"10.1109\/TCYB.2020.3020087","volume":"52","author":"X-W Zhang","year":"2022","unstructured":"Zhang, X.-W., Wu, H.-N.: Fuzzy control design of nonlinear time-delay parabolic PDE systems under mobile collocated actuators and sensors. IEEE Trans. Cybern. 52(5), 3947\u20133956 (2022)","journal-title":"IEEE Trans. Cybern."},{"issue":"5","key":"1409_CR24","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1109\/TFUZZ.2021.3061142","volume":"30","author":"Z-P Wang","year":"2022","unstructured":"Wang, Z.-P., Wu, H.-N., Huang, T.: Spatially local piecewise fuzzy control for nonlinear delayed DPSs with random packet losses. IEEE Trans. Fuzzy Syst. 30(5), 1447\u20131459 (2022)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1409_CR25","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3105249","author":"Z-P Wang","year":"2021","unstructured":"Wang, Z.-P., Zhang, X., Wu, H.-N., Huang, T.: Fuzzy boundary control for nonlinear delayed DPSs under boundary measurements. IEEE Trans. Cybern. (2021). https:\/\/doi.org\/10.1109\/TCYB.2021.3105249","journal-title":"IEEE Trans. Cybern."},{"issue":"15","key":"1409_CR26","doi-asserted-by":"publisher","first-page":"2832","DOI":"10.1080\/00207721.2014.880193","volume":"46","author":"W-H Chen","year":"2015","unstructured":"Chen, W.-H., Wang, Z., Wei, D., Lu, X.: Robust sampled-data $$H_{\\infty }$$ control of uncertain singularly perturbed systems using time-dependent lyapunov functionals. Int. J. Syst. Sci. 46(15), 2832\u20132852 (2015)","journal-title":"Int. J. Syst. Sci."},{"issue":"3","key":"1409_CR27","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1109\/TSMCB.2012.2185046","volume":"42","author":"J-W Wang","year":"2012","unstructured":"Wang, J.-W., Wu, H.-N., Li, H.-X.: Distributed proportional-spatial derivative control of nonlinear parabolic systems via fuzzy PDE modeling approach. IEEE Trans. Cybern. 42(3), 927\u2013938 (2012)","journal-title":"IEEE Trans. Cybern."},{"key":"1409_CR28","volume-title":"LMI Control Toolbox","author":"P Gahinet","year":"1995","unstructured":"Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. MathWorks, Inc., Natick (1995)"},{"key":"1409_CR29","volume-title":"Quantum Chemistry","author":"IN Levine","year":"2009","unstructured":"Levine, I.N.: Quantum Chemistry. Prentice Hall International, Inc., New York (2009)"},{"issue":"5","key":"1409_CR30","doi-asserted-by":"publisher","first-page":"2433","DOI":"10.1109\/TCYB.2019.2923461","volume":"51","author":"J-W Wang","year":"2021","unstructured":"Wang, J.-W., Wu, H.-N.: Design of suboptimal local piecewise fuzzy controller with multiple constraints for quasi-linear spatiotemporal dynamic systems. IEEE Trans. Cybern. 51(5), 2433\u20132445 (2021)","journal-title":"IEEE Trans. Cybern."},{"issue":"7","key":"1409_CR31","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1109\/TAC.2007.900823","volume":"52","author":"I Aksikas","year":"2007","unstructured":"Aksikas, I., Winkin, J.J., Dochain, D.: Optimal LQ-feedback regulation of a nonisothermal plug flow reactor model by spectral factorization. IEEE Trans. Autom. Control 52(7), 1179\u20131193 (2007)","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-022-01409-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-022-01409-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-022-01409-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T20:26:15Z","timestamp":1678825575000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-022-01409-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,6]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["1409"],"URL":"https:\/\/doi.org\/10.1007\/s40815-022-01409-6","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,6]]},"assertion":[{"value":"6 June 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}