{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T18:57:24Z","timestamp":1757617044990,"version":"3.44.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T00:00:00Z","timestamp":1726531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T00:00:00Z","timestamp":1726531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2021203069","F2022203043"],"award-info":[{"award-number":["F2021203069","F2022203043"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62103356"],"award-info":[{"award-number":["62103356"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Oversea Talents Foundation of Hebei Province","award":["C20210319"],"award-info":[{"award-number":["C20210319"]}]},{"name":"Science and Technology Project of Hebei Education Department","award":["BJK2022040"],"award-info":[{"award-number":["BJK2022040"]}]},{"name":"Science and Technology Foundation of Qinhuangdao","award":["202301A295"],"award-info":[{"award-number":["202301A295"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>This paper concerns the stability and non-weighted <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$L_2$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-gain analysis issues for the switched systems subject to asynchronous switching and external disturbance. By taking full advantage of the admissible edge-dependent average dwell time (AED-ADT) switching signal, a stability criterion of asynchronously switched systems is proposed to achieve a lower non-weighted <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$L_2$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-gain index than the existing results. Furthermore, the dynamics of switched systems are described by using the polynomial fuzzy model instead of the T-S fuzzy model, which can represent a wider range of nonlinear plants. For such asynchronously switched polynomial fuzzy systems, the relaxed conditions are derived through the membership-function-dependent (MFD) technique and novel high-order multiple Lyapunov functions (MLFs) construction method to guarantee less conservative stability and non-weighted <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$L_2$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-gain results. Finally, the superiority of the proposed approaches are verified through two simulation examples.<\/jats:p>","DOI":"10.1007\/s40815-024-01840-x","type":"journal-article","created":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T07:55:43Z","timestamp":1726732543000},"page":"1373-1389","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Relaxed Stability and Non-weighted $$L_2$$-Gain Analysis for Asynchronously Switched Polynomial Fuzzy Systems"],"prefix":"10.1007","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0467-8495","authenticated-orcid":false,"given":"Zhiyong","family":"Bao","sequence":"first","affiliation":[]},{"given":"Hak-Keung","family":"Lam","sequence":"additional","affiliation":[]},{"given":"Xiaomiao","family":"Li","sequence":"additional","affiliation":[]},{"given":"Fucai","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"issue":"2","key":"1840_CR1","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1109\/TIE.2015.2504043","volume":"63","author":"HJ Savino","year":"2016","unstructured":"Savino, H.J., Dos Santos, C.R.P., Souza, F.O., Pimenta, L.C.A., De Oliveira, M., Palhares, R.M.: Conditions for consensus of multi-agent systems with time-delays and uncertain switching topology. IEEE Trans. Ind. Electron. 63(2), 1258\u20131267 (2016)","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"9","key":"1840_CR2","doi-asserted-by":"publisher","first-page":"7161","DOI":"10.1109\/TIE.2017.2688958","volume":"64","author":"X Wang","year":"2017","unstructured":"Wang, X., Zhao, J.: Autonomous switched control of load shifting robot manipulators. IEEE Trans. Ind. Electron. 64(9), 7161\u20137170 (2017)","journal-title":"IEEE Trans. Ind. Electron."},{"key":"1840_CR3","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.nahs.2018.05.006","volume":"30","author":"W Xiang","year":"2018","unstructured":"Xiang, W., Kanjian, Z., Ming, C.: Optimal control of constrained switched systems and application to electrical vehicle energy management. Nonlinear Anal. Hybrid Syst. 30, 171\u2013188 (2018)","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"1840_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-44830-5","volume-title":"Control Synthesis of Switched Systems","author":"X Zhao","year":"2017","unstructured":"Zhao, X., Kao, Y., Niu, B., Wu, T.: Control Synthesis of Switched Systems. Springer, Berlin (2017)"},{"issue":"15","key":"1840_CR5","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.1080\/00207170500274966","volume":"78","author":"G Zhai","year":"2006","unstructured":"Zhai, G., Lin, H., Kim, Y., Imae, J., Kobayashi, T.: $${L}_2$$ gain analysis for switched systems with continuous-time and discrete-time subsystems. Int. J. Control 78(15), 1198\u20131205 (2006)","journal-title":"Int. J. Control"},{"issue":"6","key":"1840_CR6","doi-asserted-by":"publisher","first-page":"2305","DOI":"10.1109\/TSMC.2018.2794738","volume":"50","author":"L Liu","year":"2020","unstructured":"Liu, L., Zhao, X., Sun, X., Zong, G.: Stability and $$l_2$$-gain analysis of discrete-time switched systems with mode-dependent average dwell time. IEEE Trans. Syst. Man Cybern. 50(6), 2305\u20132314 (2020)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"1840_CR7","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.nahs.2018.10.001","volume":"31","author":"G Ma","year":"2019","unstructured":"Ma, G., Pagilla, P.R.: Periodic event-triggered dynamic output feedback control of switched systems. Nonlinear Anal. Hybrid Syst. 31, 247\u2013264 (2019)","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"1840_CR8","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.automatica.2015.02.010","volume":"54","author":"L Zhang","year":"2015","unstructured":"Zhang, L., Zhuang, S., Shi, P.: Non-weighted quasi-time-dependent $${H}_\\infty $$ filtering for switched linear systems with persistent dwell-time. Automatica 54, 201\u2013209 (2015)","journal-title":"Automatica"},{"issue":"11","key":"1840_CR9","doi-asserted-by":"publisher","first-page":"1874","DOI":"10.1109\/TSMC.2017.2789186","volume":"48","author":"H Ren","year":"2018","unstructured":"Ren, H., Zong, G., Li, T.: Event-triggered finite-time control for networked switched linear systems with asynchronous switching. IEEE Trans. Syst. Man Cybern. 48(11), 1874\u20131884 (2018)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"issue":"7","key":"1840_CR10","doi-asserted-by":"publisher","first-page":"4545","DOI":"10.1109\/TCYB.2022.3208156","volume":"53","author":"Q Qi","year":"2023","unstructured":"Qi, Q., Yang, X., Xu, Z., Zhang, M., Huang, T.: Novel LKF method on $$h_\\infty $$ synchronization of switched time-delay systems. IEEE Trans. Cybern. 53(7), 4545\u20134554 (2023)","journal-title":"IEEE Trans. Cybern."},{"key":"1840_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2021.101105","volume":"43","author":"Y Liu","year":"2021","unstructured":"Liu, Y., Chen, X., Lu, J., Gui, W.: Non-weighted $$l_2$$\/$${L}_2$$-gain of asynchronously switched systems. Nonlinear Anal. Hybrid Syst. 43, 101105 (2021)","journal-title":"Nonlinear Anal. Hybrid Syst."},{"issue":"1","key":"1840_CR12","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1109\/TFUZZ.2020.3031027","volume":"30","author":"S Shi","year":"2022","unstructured":"Shi, S., Fei, Z., Karimi, H.R., Lam, H.-K.: Event-triggered control for switched T-S fuzzy systems with general asynchronism. IEEE Trans. Fuzzy Syst. 30(1), 27\u201338 (2022)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"9","key":"1840_CR13","doi-asserted-by":"publisher","first-page":"2579","DOI":"10.1109\/TCYB.2016.2558821","volume":"47","author":"T Wang","year":"2017","unstructured":"Wang, T., Tong, S.: Observer-based output-feedback asynchronous control for switched fuzzy systems. IEEE Trans. Cybern. 47(9), 2579\u20132591 (2017)","journal-title":"IEEE Trans. Cybern."},{"key":"1840_CR14","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.nahs.2017.08.006","volume":"27","author":"S Li","year":"2018","unstructured":"Li, S., Xiang, Z.: Exponential stability analysis and $${L}_2$$-gain control synthesis for positive switched T-S fuzzy systems. Nonlinear Anal. Hybrid Syst. 27, 77\u201391 (2018)","journal-title":"Nonlinear Anal. Hybrid Syst."},{"issue":"8","key":"1840_CR15","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1109\/TFUZZ.2019.2917177","volume":"28","author":"M Zhang","year":"2020","unstructured":"Zhang, M., Shi, P., Shen, C., Wu, Z.G.: Static output feedback control of switched nonlinear systems with actuator faults. IEEE Trans. Fuzzy Syst. 28(8), 1600\u20131609 (2020)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"8","key":"1840_CR16","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1109\/TFUZZ.2019.2917667","volume":"28","author":"S Shi","year":"2020","unstructured":"Shi, S., Fei, Z., Shi, P., Ahn, C.K.: Asynchronous filtering for discrete-time switched T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 28(8), 1531\u20131541 (2020)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"2","key":"1840_CR17","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TSMC.2018.2882630","volume":"51","author":"Z Fei","year":"2021","unstructured":"Fei, Z., Shi, S., Wang, T., Ahn, C.K.: Improved stability criteria for discrete-time switched T-S fuzzy systems. IEEE Trans. Syst. Man Cybern. 51(2), 712\u2013720 (2021)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"issue":"1","key":"1840_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TFUZZ.2022.3180223","volume":"31","author":"Z Bao","year":"2023","unstructured":"Bao, Z., Lam, H., Peng, Y., Liu, F., Mehran, K.: Stability and stabilization of polynomial fuzzy-model-based switched nonlinear systems under MDADT switching signal. IEEE Trans. Fuzzy Syst. 31(1), 1\u201313 (2023)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"1","key":"1840_CR19","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1109\/TFUZZ.2023.3289650","volume":"32","author":"X Li","year":"2024","unstructured":"Li, X., Shan, Y., Lam, H.-K., Bao, Z., Zhao, J.: Exponential stabilization of polynomial fuzzy positive switched systems with time delay considering MDADT switching signal. IEEE Trans. Fuzzy Syst. 32(1), 174\u2013187 (2024)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1840_CR20","doi-asserted-by":"crossref","unstructured":"Sala, A., Ari\u00f1o, C.: Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya\u2019s theorem. Fuzzy Sets Syst. 158(24), 2671\u20132686 (2007)","DOI":"10.1016\/j.fss.2007.06.016"},{"issue":"6","key":"1840_CR21","doi-asserted-by":"publisher","first-page":"2993","DOI":"10.1109\/TCYB.2019.2956495","volume":"51","author":"Y-J Chen","year":"2021","unstructured":"Chen, Y.-J., Tanaka, K., Tanaka, M., Tsai, S.-H., Wang, H.O.: A novel path-following-method-based polynomial fuzzy control design. IEEE Trans. Cybern. 51(6), 2993\u20133003 (2021)","journal-title":"IEEE Trans. Cybern."},{"issue":"11","key":"1840_CR22","doi-asserted-by":"publisher","first-page":"3280","DOI":"10.1109\/TFUZZ.2020.3018185","volume":"29","author":"Z Bao","year":"2021","unstructured":"Bao, Z., Li, X., Lam, H.K., Peng, Y., Liu, F.: Membership-function-dependent stability analysis for polynomial-fuzzy-model-based control systems via Chebyshev membership functions. IEEE Trans. Fuzzy Syst. 29(11), 3280\u20133292 (2021)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"5","key":"1840_CR23","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1016\/j.automatica.2010.02.021","volume":"46","author":"L Zhang","year":"2010","unstructured":"Zhang, L., Gao, H.: Asynchronously switched control of switched linear systems with average dwell time. Automatica 46(5), 953\u2013958 (2010)","journal-title":"Automatica"},{"key":"1840_CR24","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/j.isatra.2020.04.012","volume":"103","author":"C Liu","year":"2020","unstructured":"Liu, C., Li, Y., Zheng, Q., Zhang, H.: Non-weighted $${L}_2$$ gain and asynchronous $${H}_\\infty $$ control for continuous-time switched T-S fuzzy systems. ISA Trans. 103, 228\u2013236 (2020)","journal-title":"ISA Trans."},{"key":"1840_CR25","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/j.ins.2012.12.027","volume":"232","author":"HK Lam","year":"2013","unstructured":"Lam, H.K., Lauber, J.: Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions. Inf. Sci. 232, 253\u2013266 (2013)","journal-title":"Inf. Sci."},{"key":"1840_CR26","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.nahs.2018.01.003","volume":"29","author":"J Yang","year":"2018","unstructured":"Yang, J., Zhao, X., Bu, X., Qian, W.: Stabilization of switched linear systems via admissible edge-dependent switching signals. Nonlinear Anal. Hybrid Syst. 29, 100\u2013109 (2018)","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"1840_CR27","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1016\/j.engappai.2017.09.007","volume":"67","author":"HK Lam","year":"2018","unstructured":"Lam, H.K.: A review on stability analysis of continuous-time fuzzy-model-based control systems: from membership-function-independent to membership-function-dependent analysis. Eng. Appl. Artif. Intell. 67, 390\u2013408 (2018)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"1840_CR28","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.automatica.2017.10.018","volume":"87","author":"S Yuan","year":"2018","unstructured":"Yuan, S., Zhang, L., De Schutter, B., Baldi, S.: A novel Lyapunov function for a non-weighted $${L}_2$$ gain of asynchronously switched linear systems. Automatica 87, 310\u2013317 (2018)","journal-title":"Automatica"},{"issue":"5","key":"1840_CR29","doi-asserted-by":"publisher","first-page":"2873","DOI":"10.1109\/TFUZZ.2017.2786211","volume":"26","author":"J-C Lo","year":"2018","unstructured":"Lo, J.-C., Lin, C.: Polynomial fuzzy observed-state feedback stabilization via homogeneous Lyapunov methods. IEEE Trans. Fuzzy Syst. 26(5), 2873\u20132885 (2018)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"4","key":"1840_CR30","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1109\/TFUZZ.2019.2914005","volume":"28","author":"B Jiang","year":"2020","unstructured":"Jiang, B., Karimi, H.R., Kao, Y., Gao, C.: Takagi-Sugeno model based event-triggered fuzzy sliding-mode control of networked control systems with semi-markovian switchings. IEEE Trans. Fuzzy Syst. 28(4), 673\u2013683 (2020)","journal-title":"IEEE Trans. Fuzzy Syst."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01840-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-024-01840-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01840-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T22:30:46Z","timestamp":1757111446000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-024-01840-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,17]]},"references-count":30,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["1840"],"URL":"https:\/\/doi.org\/10.1007\/s40815-024-01840-x","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"type":"print","value":"1562-2479"},{"type":"electronic","value":"2199-3211"}],"subject":[],"published":{"date-parts":[[2024,9,17]]},"assertion":[{"value":"10 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known Conflict of interest or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}