{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:14:48Z","timestamp":1760148888845,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T00:00:00Z","timestamp":1686528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"],"award-info":[{"award-number":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"],"award-info":[{"award-number":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"]}]},{"name":"Science and Technology Research Project of Chongqing Municipal Education Commission","award":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"],"award-info":[{"award-number":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"]}]},{"name":"the High-level Talents Research Project of CTBU","award":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"],"award-info":[{"award-number":["62003062","62241201","2022YFE0107300","KJZD-M201900801","KJQN201900831","1953013","1956030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we investigate the problem of a dynamic event-triggered robust controller design for flexible robotic arm systems with continuous-time phase-type semi-Markov jump process. In particular, the change in moment of inertia is first considered in the flexible robotic arm system, which is necessary for ensuring the security and stability control of special robots employed under special circumstances, such as surgical robots and assisted-living robots which have strict lightweight requirements. To handle this problem, a semi-Markov chain is conducted to model this process. Furthermore, the dynamic event-triggered scheme is used to solve the problem of limited bandwidth in the network transmission environment, while considering the impact of DoS attacks. With regard to the challenging circumstances and negative elements previously mentioned, the adequate criteria for the existence of the resilient H\u221e controller are obtained using the Lyapunov function approach, and the controller gains, Lyapunov parameters and event-triggered parameters are co-designed. Finally, the effectiveness of the designed controller is demonstrated via numerical simulation using the LMI toolbox in MATLAB.<\/jats:p>","DOI":"10.3390\/s23125523","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T02:00:45Z","timestamp":1686621645000},"page":"5523","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Improved Dynamic Event-Triggered Robust Control for Flexible Robotic Arm Systems with Semi-Markov Jump Process"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3406-8954","authenticated-orcid":false,"given":"Huiyan","family":"Zhang","sequence":"first","affiliation":[{"name":"National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China"},{"name":"National Engineering Laboratory for Industrial Big-Data Application Technology, Chongqing Innovation Center of Industrial Big-Data Co., Ltd., Chongqing 400707, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9013-6299","authenticated-orcid":false,"given":"Zixian","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering Chongqing Technology and Business University, Chongqing 400067, China"}]},{"given":"Wengang","family":"Ao","sequence":"additional","affiliation":[{"name":"National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8218-586X","authenticated-orcid":false,"given":"Peng","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, SA 5005, Australia"},{"name":"School of Information Science and Technology, Fujian University of Technology, Fuzhou 350118, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3836","DOI":"10.1109\/TCSI.2021.3091533","article-title":"Uncertain disturbance rejection and attenuation for semi-Markov jump systems with application to 2-degree-freedom robot arm","volume":"68","author":"Yao","year":"2021","journal-title":"IEEE Trans. Circuits Syst. Regul. Pap."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1109\/TCYB.2022.3163271","article-title":"Hybrid dynamic event-triggered load frequency control for power systems with unreliable transmission networks","volume":"53","author":"Liu","year":"2022","journal-title":"IEEE Trans. Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1109\/TSTE.2015.2393353","article-title":"A semi-Markov model for control of energy storage in utility grids and microgrids with PV generation","volume":"6","author":"Barnes","year":"2015","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1109\/TAC.2019.2913050","article-title":"Reduced-order observer design for switched descriptor systems with unknown inputs","volume":"65","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12555-014-0576-4","article-title":"A survey on Markovian jump systems: Modeling and design","volume":"13","author":"Shi","year":"2015","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Serafini, A.R.C., Delforno, L., Palma, J.M., Behrens, F.H., and Morais, C.F. (2021). Robust static output-feedback control for MJLS with non-homogeneous Markov chains: A comparative study considering a wireless sensor network with time-varying PER. Sensors, 21.","DOI":"10.3390\/s21196420"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1250","DOI":"10.1109\/TAC.2018.2846594","article-title":"Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity","volume":"64","author":"Dong","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.3390\/s140101835","article-title":"Markov jump linear systems-based position estimation for lower limb exoskeletons","volume":"14","author":"Nogueira","year":"2014","journal-title":"Sensors"},{"key":"ref_9","first-page":"319","article-title":"Adaptive H\u221e sliding mode control for a class of uncertain Markovian jump systems with time-delay","volume":"14","author":"Liu","year":"2020","journal-title":"ICIC Express Lett."},{"key":"ref_10","first-page":"390","article-title":"Stochastic stabilization of singular systems with Markovian switchings","volume":"250","author":"Wang","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sysconle.2018.02.004","article-title":"Admissibility and stabilization of stochastic singular Markovian jump systems with time delays","volume":"114","author":"Zhuang","year":"2018","journal-title":"Syst. Control Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1109\/TAC.2006.878746","article-title":"Stochastic stability of Ito differential equations with semi-Markovian jump parameters","volume":"51","author":"Hou","year":"2006","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3317","DOI":"10.1002\/rnc.3057","article-title":"Stochastic stability of semi-Markovian jump systems with mode-dependent delays","volume":"24","author":"Li","year":"2014","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1109\/TCYB.2020.2981158","article-title":"Asynchronous adaptive fault-tolerant sliding-mode control for T\u2013S fuzzy singular Markovian jump systems with uncertain transition rates","volume":"52","author":"Li","year":"2022","journal-title":"IEEE Trans. Cybern."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2225","DOI":"10.1109\/TSMC.2020.3049137","article-title":"Filter for positive stochastic nonlinear switching systems with phase-type semi-Markov parameters and application","volume":"52","author":"Qi","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5213","DOI":"10.1002\/rnc.4679","article-title":"Observer-based mode-independent integral sliding mode controller design for phase-type semi-Markov jump singular systems","volume":"29","author":"Li","year":"2019","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1109\/TCYB.2022.3168854","article-title":"Dynamic self-triggered impulsive synchronization of complex networks with mismatched parameters and distributed delay","volume":"53","author":"Ding","year":"2023","journal-title":"IEEE Trans. Cybern."},{"key":"ref_18","first-page":"243","article-title":"Observer-based controller design for networked control systems with induced delays and data packet dropouts","volume":"12","author":"Zhang","year":"2021","journal-title":"ICIC Express Lett. Part Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"101465","DOI":"10.1109\/ACCESS.2022.3208136","article-title":"Finite-time H\u221e robust controller design for a class of singular discrete-time Markov jump delay systems with packet loss compensation and input saturation","volume":"10","author":"Zhao","year":"2022","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7343","DOI":"10.1016\/j.jfranklin.2020.04.058","article-title":"Fault detection filters design of polytopic uncertain discrete-time singular Markovian jump systems with time-varying delays","volume":"357","author":"Shi","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_21","first-page":"8687","article-title":"A simple event-based PID controller","volume":"32","year":"1999","journal-title":"ICIC Proc. Vol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1109\/TAC.2012.2206694","article-title":"A delay system method for designing event-triggered controllers of networked control systems","volume":"58","author":"Yue","year":"2012","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1002\/rnc.4403","article-title":"Dynamic event-triggered control for linear time-invariant systems with-gain performance","volume":"29","author":"Liu","year":"2019","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1109\/TAC.2014.2366855","article-title":"Dynamic triggering mechanisms for event-triggered control","volume":"60","author":"Girard","year":"2014","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Sathishkumar, M., and Liu, Y.-C. (2023). Resilient finite-time distributed event-triggered consensus of multi-agent systems with multiple cyber-attacks. Commun. Nonlinear Sci. Numer. Simul., 116.","DOI":"10.1016\/j.cnsns.2022.106876"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"92288","DOI":"10.1109\/ACCESS.2021.3092402","article-title":"Resilient annular finite-time bounded and adaptive event-triggered control for networked switched systems with deception attacks","volume":"9","author":"Sathishkumar","year":"2021","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1109\/TSMC.2019.2900502","article-title":"A novel robust control method for motion control of uncertain single-link flexible-joint manipulator","volume":"51","author":"Yan","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/TAC.2022.3142123","article-title":"Semiglobal periodic event-triggered output regulation for nonlinear multiagent systems","volume":"68","author":"Zheng","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1109\/TFUZZ.2018.2886158","article-title":"Event-triggered robust adaptive fuzzy control for a class of nonlinear systems","volume":"27","author":"Wang","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.neucom.2015.04.107","article-title":"Adaptive event-triggered communication scheme for networked control systems with randomly occurring nonlinearities and uncertainties","volume":"174","author":"Zhang","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Zhao, N., Zhao, X., Xu, N., and Zhang, L. (2023). Resilient event-triggered control of connected automated vehicles under cyber attacks. IEEE\/CAA J. Autom. Sin., 1\u20133.","DOI":"10.1109\/JAS.2023.123483"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhang, H., Zhao, N., Wang, S., and Agarwal, R.K. (2023). Improved Event-Triggered Dynamic Output Feedback Control for Networked T\u2013S Fuzzy Systems with Actuator Failure and Deception Attacks. IEEE Trans. Cybern., 1\u201311.","DOI":"10.1109\/TCYB.2023.3264820"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Gu, K., Chen, J., and Kharitonov, V.L. (2003). Stability of Time-Delay Systems, Springer Science & Business Media.","DOI":"10.1007\/978-1-4612-0039-0"},{"key":"ref_34","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_35","unstructured":"Kushner, H.J. (1967). Stochastic Stability and Control, Brown Univ Providence RI. Technical Report."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5523\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:53:29Z","timestamp":1760126009000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5523"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,12]]},"references-count":35,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["s23125523"],"URL":"https:\/\/doi.org\/10.3390\/s23125523","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,6,12]]}}}