{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:15:56Z","timestamp":1763975756890,"version":"3.45.0"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T00:00:00Z","timestamp":1763769600000},"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":["62403227","12201280","62273172"],"award-info":[{"award-number":["62403227","12201280","62273172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2023MF065"],"award-info":[{"award-number":["ZR2023MF065"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper studies discrete-time semi-Markov neural networks (NNs) and proposes a finite-time \u03b3-dissipative fault estimate (FE) and fault-tolerant synchronization control (FTSC) with the event-triggered method. Based on the intermediate variable introduced, an FE scheme is presented to obtain estimate information of faults, states, and intermediate variables. According to the event-triggered condition designed, an FTSC protocol is proposed so that the error system between master system and slave system is stochasticslly synchronized within finite time and meets \u03b3-dissipativity. An example shows the validity of this proposed scheme.<\/jats:p>","DOI":"10.3390\/e27121186","type":"journal-article","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:02:07Z","timestamp":1763974927000},"page":"1186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite-Time Dissipative Fault Estimate and Event-Triggered Fault-Tolerant Synchronization Control for Discrete Semi-Markov Jumping Neural Networks"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6177-5729","authenticated-orcid":false,"given":"Xiaodan","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-4706-8853","authenticated-orcid":false,"given":"Yanjun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7042-680X","authenticated-orcid":false,"given":"Yu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Chemistry and Chemical Engineering, Ludong University, Yantai 264025, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,22]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Exponential synchronization of neural networks with time-varying delays via dynamic intermittent output feedback control","volume":"99","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_2","first-page":"970","article-title":"Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality","volume":"5","author":"Zhang","year":"2017","journal-title":"Int. J. Syst. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/j.neucom.2020.10.063","article-title":"Extended dissipativity of semi-Markov jump neural networks with partly unknown transition rates","volume":"423","author":"Chen","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.neucom.2019.03.041","article-title":"Extended disspative synchronization for singularly perturbed semi-Markov jump neural networks with randomly occurring uncertainties","volume":"349","author":"Wang","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6352","DOI":"10.1016\/j.jfranklin.2020.03.031","article-title":"Non-fragile mixed passive and H\u221e state estimation for singularly perturbed neural networks with semi-Markov jumping parameters","volume":"357","author":"Shen","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.neunet.2018.05.007","article-title":"Event-triggered H\u221e state estimation for semi-Markov jumping discrete-time neural networks with quantization","volume":"105","author":"Rakkiyappan","year":"2018","journal-title":"Neural Netw."},{"key":"ref_7","first-page":"529","article-title":"On stability of motion over a finite interval of time [in Russian]","volume":"17","author":"Kamenkov","year":"1953","journal-title":"J. Appl. Math. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yang, P., Ding, Y., Shen, Z.W., and Feng, K.J. (2022). Integral non-singular terminal sliding mode consensus control for multi-agent systems with disturbance and actuator faults based on finite-time observer. Entropy, 24.","DOI":"10.3390\/e24081068"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1016\/j.jfranklin.2020.12.013","article-title":"Stochastic H\u221e finite-time control for linear neutral semi-Markovian jumping systems under event-triggering scheme","volume":"358","author":"Ju","year":"2021","journal-title":"J. Frankl. Inst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10626","DOI":"10.1016\/j.jfranklin.2020.08.036","article-title":"Event-triggered non-fragile finite-time H\u221e control for semi-Markovian jump systems with actuator saturation","volume":"357","author":"Luo","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.neucom.2020.10.088","article-title":"Time-varying delay-dependent finite-time boundedness with H\u221e performance for Markovian jump neural networks with state and input constraints","volume":"423","author":"Sun","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1007\/s11071-014-1412-3","article-title":"Finite-time synchronization control for uncertain Markov jump neural networks with input constraints","volume":"77","author":"Shen","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_13","first-page":"467","article-title":"Non-fragile finite-time l2\u2013l\u221e state estimation for discrete-time Markov jump neural networks with unreliable communication links","volume":"271","author":"Li","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.neucom.2015.03.034","article-title":"Finite-time H\u221e synchronization control for semi-Markov jump delayed neural networks with randomly occurring uncertainties","volume":"166","author":"Li","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_15","first-page":"230","article-title":"Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties","volume":"344-345","author":"Zhang","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/TNSE.2020.3032025","article-title":"Finite-time L2-L\u221e synchronization for semi-Markov jump inertial neural networks using sampled data","volume":"8","author":"Wang","year":"2021","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/0005-1098(71)90007-0","article-title":"A heuristic approach to the design of linear multivariable interacting control systems","volume":"7","author":"Niederlinski","year":"1971","journal-title":"Automatica"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Liu, L.J., Lv, J.L., Lin, H.W., Zhan, R.D., and Wu, L.M. (2025). ADP-based fault-tolerant control with stability guarantee for nonlinear systems. Entropy, 27.","DOI":"10.3390\/e27101028"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6233","DOI":"10.1002\/rnc.6694","article-title":"Finite-time fault estimate and fault-tolerant control for discrete-time Markov jump systems with actuator and sensor faults","volume":"33","author":"Zhu","year":"2023","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3612","DOI":"10.1016\/j.jfranklin.2019.02.025","article-title":"Reliable consensus control for semi-Markov jump multi-agent systems: A leader following strategy","volume":"356","author":"Wang","year":"2019","journal-title":"J. Frankl. Inst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.ins.2020.08.098","article-title":"Reliable observer-based finite-time H\u221e control for networked nonlinear semi-Markovian jump systems with actuator fault and parameter uncertainties via dynamic event-triggered scheme","volume":"546","author":"Mu","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.neucom.2014.06.022","article-title":"Passivity-based fault-tolerant synchronization control of chaotic neural networks against actuator faults using the semi-Markov jump model approach","volume":"143","author":"Wang","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.neunet.2020.02.015","article-title":"Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters","volume":"125","author":"Zhou","year":"2020","journal-title":"Neural Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.physleta.2006.03.078","article-title":"Exponential stability of delayed recurrent neural networks with Markovian jumping parameters","volume":"356","author":"Wang","year":"2006","journal-title":"Phys. Lett. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2518","DOI":"10.1109\/TAC.2015.2491898","article-title":"Fault estimation for a class of nonlinear systems based on intermediate estimator","volume":"61","author":"Zhu","year":"2016","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/TCNS.2016.2567223","article-title":"Robust distributed fault estimation for a network of dynamical systems","volume":"5","author":"Zhu","year":"2018","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7426","DOI":"10.1109\/TII.2019.2958988","article-title":"Intermediate observer based robust distributed fault estimation for nonlinear multi-agent systems with directed graphs","volume":"16","author":"Han","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.automatica.2018.12.006","article-title":"Fault detection filtering for nonlinear switched systems via event-triggered communication approach","volume":"101","author":"Liu","year":"2019","journal-title":"Automatica"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1049\/iet-cta.2011.0335","article-title":"Finite\u2013time stochastic stability and stabilisation of linear discrete-time Markovian jump systems with partly unknown transition probabilities","volume":"6","author":"Zuo","year":"2012","journal-title":"IET Control Theory Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1109\/TAC.2015.2477976","article-title":"Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation","volume":"61","author":"Shi","year":"2016","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0167-6911(92)90097-C","article-title":"Robust control of a class of uncertain nonlinear systems","volume":"19","author":"Wang","year":"1992","journal-title":"Syst. Control Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gu, K., Chen, J., and Kharitonov, V.L. (2003). Stability of Time-Delay Systems, Springer Science and Business Media.","DOI":"10.1007\/978-1-4612-0039-0"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1109\/TAC.2008.2008319","article-title":"Stabilization of networked control systems with a logic ZOH","volume":"54","author":"Xiong","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_34","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"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/12\/1186\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:13:01Z","timestamp":1763975581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/12\/1186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,22]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["e27121186"],"URL":"https:\/\/doi.org\/10.3390\/e27121186","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,22]]}}}