{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T10:11:51Z","timestamp":1780049511925,"version":"3.53.1"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"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":["J Syst Sci Complex"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s11424-025-4131-6","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T10:44:49Z","timestamp":1749465889000},"page":"1047-1071","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Proportional-Integral Observer-Based PID Control of Positive Switched Systems"],"prefix":"10.1007","volume":"38","author":[{"given":"Wei","family":"Xing","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyue","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junfeng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuan","family":"Jia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,6,9]]},"reference":[{"key":"4131_CR1","volume-title":"An Introduction to Hybrid Dynamical Systems","author":"A J Van Der Schaft","year":"2007","unstructured":"Van Der Schaft A J and Schumacher H, An Introduction to Hybrid Dynamical Systems, Springer, New York, 2007."},{"key":"4131_CR2","volume-title":"Introduction to Dynamic Systems","author":"D Lunberger","year":"1979","unstructured":"Lunberger D, Introduction to Dynamic Systems, Wiley, New York, 1979."},{"key":"4131_CR3","doi-asserted-by":"publisher","DOI":"10.1002\/9781118033029","volume-title":"Positive Linear Systems: Theory and Applications","author":"L Farinan","year":"2000","unstructured":"Farinan L and Rinaldi S, Positive Linear Systems: Theory and Applications, Wiley, New York, 2000."},{"key":"4131_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0221-2","volume-title":"Positive 1D and 2D Systems","author":"T Kaczorek","year":"2002","unstructured":"Kaczorek T, Positive 1D and 2D Systems, Springer-Verlag, London, UK, 2002."},{"issue":"2","key":"4131_CR5","first-page":"151","volume":"54","author":"M A Rami","year":"2007","unstructured":"Rami M A and Tadeo F, Controller synthesis for positive linear systems with bounded controls, IEEE Transactions on Circuits and Systems II: Express Briefs, 2007, 54(2): 151\u2013155.","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"issue":"2","key":"4131_CR6","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1109\/TAC.2022.3146709","volume":"68","author":"J Zhang","year":"2023","unstructured":"Zhang J, Zheng G, Feng Y, et al., Event-triggered state-feedback and dynamic output-feedback control of positive Markovian jump systems with intermittent faults, IEEE Transactions on Automatic Control, 2023, 68(2): 1039\u20131046.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"4131_CR7","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/j.automatica.2015.10.025","volume":"63","author":"J Shen","year":"2016","unstructured":"Shen J and Lam J, Static output-feedback stabilization with optimal L1-gain for positive linear systems, Automatica, 2016, 63: 248\u2013253.","journal-title":"Automatica"},{"key":"4131_CR8","volume-title":"Proceedings of 12th Yale Workshop on Adaptive and Learning Systems","author":"R Shorten","year":"2003","unstructured":"Shorten R, Leith D, Foy J, et al., Analysis and design of synchronised communication networks, Proceedings of 12th Yale Workshop on Adaptive and Learning Systems, 2003."},{"key":"4131_CR9","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1109\/MED.2008.4602046","volume-title":"2008 16th Mediterranean Conference on Control and Automation","author":"A Benzaouia","year":"2008","unstructured":"Benzaouia A and Tadeo F, Output feedback stabilization of positive switching linear discrete-time systems, 2008 16th Mediterranean Conference on Control and Automation, 2008, 119\u2013124."},{"issue":"6","key":"4131_CR10","doi-asserted-by":"publisher","first-page":"1132","DOI":"10.1016\/j.automatica.2012.03.008","volume":"48","author":"X Zhao","year":"2012","unstructured":"Zhao X, Zhang L, Shi P, et al., Stability of switched positive linear systems with average dwell time switching, Automatica, 2012, 48(6): 1132\u20131137.","journal-title":"Automatica"},{"issue":"5","key":"4131_CR11","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1002\/rnc.2777","volume":"23","author":"X Zhao","year":"2013","unstructured":"Zhao X, Zhang L, and Shi P, Stability of a class of switched positive linear time-delay systems, International Journal of Robust and Nonlinear Control, 2013, 23(5): 578\u2013589.","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"4131_CR12","first-page":"9","volume":"9","author":"M Xiang","year":"2013","unstructured":"Xiang M and Xiang Z, Stability, L1-gain and control synthesis for positive switched systems with time-varying delay, Nonlinear Analysis: Hybrid Systems, 2013, 9: 9\u201317.","journal-title":"Nonlinear Analysis: Hybrid Systems"},{"issue":"3","key":"4131_CR13","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1049\/iet-cta.2012.0428","volume":"7","author":"J Zhang","year":"2013","unstructured":"Zhang J, Han Z, Zhu F, et al., Feedback control for switched positive linear systems, IET Control Theory & Applications, 2013, 7(3): 464\u2013469.","journal-title":"IET Control Theory & Applications"},{"key":"4131_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/1-84628-148-2","volume-title":"PID Control","author":"M A Johnson","year":"2005","unstructured":"Johnson M A and Moradi M H, PID Control, Springer-Verlag London Limited, UK, 2005."},{"issue":"3","key":"4131_CR15","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1016\/S0005-1098(01)00237-0","volume":"38","author":"F Zheng","year":"2002","unstructured":"Zheng F, Wang Q G, and Lee T H, On the design of multivariable PID controllers via LMI approach, Automatica, 2002, 38(3): 517\u2013526.","journal-title":"Automatica"},{"key":"4131_CR16","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.neucom.2018.12.002","volume":"332","author":"Y Wang","year":"2019","unstructured":"Wang Y, Zou L, Zhao Z, et al., H\u221e fuzzy PID control for discrete time-delayed TS fuzzy systems, Neurocomputing, 2019, 332: 91\u201399.","journal-title":"Neurocomputing"},{"issue":"10","key":"4131_CR17","doi-asserted-by":"publisher","first-page":"2168","DOI":"10.1080\/00207721.2017.1306145","volume":"48","author":"J Liu","year":"2017","unstructured":"Liu J, Lam J, Shen M, et al., Non-fragile multivariable PID controller design via system augmentation, International Journal of Systems Science, 2017, 48(10): 2168\u20132181.","journal-title":"International Journal of Systems Science"},{"key":"4131_CR18","first-page":"1","volume-title":"2020 Cybernetics & Informatics","author":"J Paulusov\u00e1","year":"2020","unstructured":"Paulusov\u00e1 J, Vesel\u00fd V, and Paulus M, Robust PI controller design for positive systems, 2020 Cybernetics & Informatics, 2020, 1\u20134."},{"key":"4131_CR19","first-page":"1593","volume-title":"2022 41st Chinese Control Conference","author":"X Zhou","year":"2022","unstructured":"Zhou X, Zhang J, Lin P, et al., Event-triggered PI control of positive switched systems, 2022 41st Chinese Control Conference, 2022, 1593\u20131598."},{"issue":"10","key":"4131_CR20","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1049\/cth2.12460","volume":"17","author":"X Zhou","year":"2023","unstructured":"Zhou X, Zhang J, Jia X, et al., Linear programming-based proportional-integral-derivative control of positive systems, IET Control Theory & Applications, 2023, 17(10): 1342\u20131353.","journal-title":"IET Control Theory & Applications"},{"issue":"6","key":"4131_CR21","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1109\/TAC.1971.1099826","volume":"16","author":"D Luenberger","year":"1971","unstructured":"Luenberger D, An introduction to observers, IEEE Transactions on Automatic Control, 1971, 16(6): 596\u2013602.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"6","key":"4131_CR22","doi-asserted-by":"publisher","first-page":"3926","DOI":"10.1109\/TSMC.2019.2952539","volume":"51","author":"D Zhao","year":"2019","unstructured":"Zhao D, Wang Z, Ho D W C, et al., Observer-based PID security control for discrete time-delay systems under cyber-attacks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 51(6): 3926\u20133938.","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"issue":"1","key":"4131_CR23","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1080\/00207178908953350","volume":"50","author":"S Beale","year":"1989","unstructured":"Beale S and Shafai B, Robust control system design with a proportional integral observer, International Journal of Control, 1989, 50(1): 97\u2013111.","journal-title":"International Journal of Control"},{"issue":"5","key":"4131_CR24","doi-asserted-by":"publisher","first-page":"814","DOI":"10.1109\/TAC.2006.875019","volume":"51","author":"J L Chang","year":"2006","unstructured":"Chang J L, Applying discrete-time proportional integral observers for state and disturbance estimations, IEEE Transactions on Automatic Control, 2006, 51(5): 814\u2013818.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"4131_CR25","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1109\/TNNLS.2022.3174880","volume":"35","author":"J Cheng","year":"2024","unstructured":"Cheng J, Liang L, Yan H, et al., Proportional-integral observer-based state estimation for Markov memristive neural networks with sensor saturations, IEEE Transactions on Neural Networks and Learning Systems, 2024, 35(1): 405\u2013416.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"issue":"3","key":"4131_CR26","doi-asserted-by":"publisher","first-page":"887","DOI":"10.1002\/rnc.5328","volume":"31","author":"D Zhao","year":"2021","unstructured":"Zhao D, Wang Z, Wei G, et al., \u21132-\u2113\u221e proportional-integral observer design for systems with mixed time-delays under round robin protocol, International Journal of Robust and Nonlinear Control, 2021, 31(3): 887\u2013906.","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"4131_CR27","first-page":"1","volume-title":"2007 Mediterranean Conference on Control & Automation","author":"M A Rami","year":"2007","unstructured":"Rami M A, Helmke U, and Tadeo F, Positive observation problem for linear time-delay positive systems, 2007 Mediterranean Conference on Control & Automation, 2007, 1\u20136."},{"key":"4131_CR28","doi-asserted-by":"publisher","first-page":"4729","DOI":"10.1109\/CDC.2006.377749","volume-title":"Proceedings of the 45th IEEE Conference on Decision and Control","author":"M A Rami","year":"2006","unstructured":"Rami M A and Tadeo F, Positive observation problem for linear discrete positive systems, Proceedings of the 45th IEEE Conference on Decision and Control, 2006, 4729\u20134733."},{"issue":"4","key":"4131_CR29","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1080\/00207179.2011.573000","volume":"84","author":"M A Rami","year":"2011","unstructured":"Rami M A, Tadeo F, and Helmke U, Positive observers for linear positive systems, and their implications, International Journal of Control, 2011, 84(4): 716\u2013725.","journal-title":"International Journal of Control"},{"issue":"1","key":"4131_CR30","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1109\/TAC.1962.1105415","volume":"7","author":"R C Dorf","year":"1962","unstructured":"Dorf R C, Farren M, and Phillips C, Adaptive sampling frequency for sampled-data control systems, IRE Transactions on Automatic Control, 1962, 7(1): 38\u201347.","journal-title":"IRE Transactions on Automatic Control"},{"issue":"11","key":"4131_CR31","doi-asserted-by":"publisher","first-page":"3532","DOI":"10.1002\/rnc.4097","volume":"28","author":"Y Yin","year":"2018","unstructured":"Yin Y, Lin Z, Liu Y, et al., Event-triggered constrained control of positive systems with input saturation, International Journal of Robust and Nonlinear Control, 2018, 28(11): 3532\u20133542.","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"1","key":"4131_CR32","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1049\/iet-cta.2019.0606","volume":"14","author":"L Liu","year":"2020","unstructured":"Liu L, Zhang J, Shao Y, et al., Event-triggered control of positive switched systems based on linear programming, IET Control Theory & Applications, 2020, 14(1): 145\u2013155.","journal-title":"IET Control Theory & Applications"},{"key":"4131_CR33","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.ins.2018.08.036","volume":"469","author":"S Xiao","year":"2018","unstructured":"Xiao S, Zhang Y, and Zhang B, Event-triggered network-based state observer design of positive systems, Information Sciences, 2018, 469: 30\u201343.","journal-title":"Information Sciences"},{"issue":"7","key":"4131_CR34","doi-asserted-by":"publisher","first-page":"1992","DOI":"10.1109\/TAC.2014.2366855","volume":"60","author":"A Girard","year":"2014","unstructured":"Girard A, Dynamic triggering mechanisms for event-triggered control, IEEE Transactions on Automatic Control, 2014, 60(7): 1992\u20131997.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"4131_CR35","doi-asserted-by":"publisher","first-page":"109128","DOI":"10.1016\/j.automatica.2020.109128","volume":"120","author":"D Zhao","year":"2020","unstructured":"Zhao D, Wang Z, Wei G, et al., A dynamic event-triggered approach to observer-based PID security control subject to deception attacks, Automatica, 2020, 120: 109128.","journal-title":"Automatica"},{"issue":"5","key":"4131_CR36","doi-asserted-by":"publisher","first-page":"2536","DOI":"10.1002\/rnc.5674","volume":"32","author":"J Wu","year":"2022","unstructured":"Wu J and Peng C, Observer-based adaptive event-triggered PID control for networked systems under aperiodic DoS attacks, International Journal of Robust and Nonlinear Control, 2022, 32(5): 2536\u20132550.","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"8","key":"4131_CR37","doi-asserted-by":"publisher","first-page":"3631","DOI":"10.1016\/j.jfranklin.2022.03.003","volume":"359","author":"K Yin","year":"2022","unstructured":"Yin K and Yang D, Output feedback l1 control of positive Markov jump systems: A dynamic event-triggered method, Journal of the Franklin Institute, 2022, 359(8): 3631\u20133655.","journal-title":"Journal of the Franklin Institute"},{"key":"4131_CR38","first-page":"101328","volume":"48","author":"J Zhang","year":"2023","unstructured":"Zhang J, Zhang S, Deng X, et al., Adaptive event-triggered dynamic distributed control of switched positive systems with switching faults, Nonlinear Analysis: Hybrid Systems, 2023, 48: 101328.","journal-title":"Nonlinear Analysis: Hybrid Systems"},{"key":"4131_CR39","first-page":"2655","volume":"3","author":"J P Hespanha","year":"1999","unstructured":"Hespanha J P and Morse A S, Stability of switched systems with average dwell-time, Proceedings of the 38th IEEE Conference on Decision and Control, 1999, 3: 2655\u20132660.","journal-title":"Proceedings of the 38th IEEE Conference on Decision and Control"},{"key":"4131_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0017-8","volume-title":"Switching in Systems and Control","author":"D Liberzon","year":"2003","unstructured":"Liberzon D, Switching in Systems and Control, Birkhauser, Boston, 2003."},{"key":"4131_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.automatica.2017.07.016","volume":"85","author":"W Xiang","year":"2017","unstructured":"Xiang W, Lam J, and Shen J, Stability analysis and L1-gain characterization for switched positive systems under dwell-time constraint, Automatica, 2017, 85: 1\u20138.","journal-title":"Automatica"},{"issue":"1","key":"4131_CR42","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1109\/MCS.2012.2225919","volume":"33","author":"C Ocampo-Martinez","year":"2013","unstructured":"Ocampo-Martinez C, Puig V, Cembrano G, et al., Application of predictive control strategies to the management of complex networks in the urban water cycle [applications of control], IEEE Control Systems Magazine, 2013, 33(1): 15\u201341.","journal-title":"IEEE Control Systems Magazine"},{"key":"4131_CR43","first-page":"4573","volume-title":"2017 36th Chinese Control Conference","author":"J Zhang","year":"2017","unstructured":"Zhang J, Jia X, Zhang R, et al., Parameter-dependent Lyapunov function based model predictive control for positive systems and its application in urban water management, 2017 36th Chinese Control Conference, 2017, 4573\u20134578."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-025-4131-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-025-4131-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-025-4131-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T15:05:18Z","timestamp":1749481518000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-025-4131-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6]]},"references-count":43,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["4131"],"URL":"https:\/\/doi.org\/10.1007\/s11424-025-4131-6","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6]]},"assertion":[{"value":"1 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}