{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:17:31Z","timestamp":1762341451317},"reference-count":52,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T00:00:00Z","timestamp":1586217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper establishes a stochastic synchronization method for a Markovian jump complex dynamical network (MJCDN) with time-delay and uncertainties. The considered Markovian structure is piecewise-homogeneous with piecewise-constant time-varying transition rates (TRs). Two Markovian signals are utilized to construct the piecewise-homogeneous Markovian structure. A low-level Markovian signal with time-varying TRs governs the switching between the system dynamics while it is managed by a high-level Markovian signal. Due to the effect of imperfections induced by modeling errors in the system dynamics, some parametric norm-bounded uncertainties are considered. In addition, uncertain TR matrix is considered which means that inaccurate or uncertain information for each element of the TR matrix is allowable. This modelling makes the MJCDN to be more general and applicable than the existing ones. Synchronization conditions are obtained and reported in the form of linear matrix inequalities by the help of Lyapunov\u2013Krasovskii theory, Wirtinger-based integral inequality approach and reciprocally convex technique. Finally, a numerical example is presented to verify the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1093\/imamci\/dnz041","type":"journal-article","created":{"date-parts":[[2020,4,3]],"date-time":"2020-04-03T19:11:39Z","timestamp":1585941099000},"page":"1168-1191","source":"Crossref","is-referenced-by-count":2,"title":["Robust exponential synchronization of a Markovian jump complex dynamical network with piecewise homogeneous Markovian parameters"],"prefix":"10.1093","volume":"37","author":[{"given":"Nasim","family":"Akbari","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran"}]},{"given":"Ali","family":"Sadr","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran"}]},{"given":"Ali","family":"Kazemy","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Tafresh University, Tafresh 39518-79611, Iran"}]}],"member":"286","published-online":{"date-parts":[[2020,4,7]]},"reference":[{"key":"2020121601135066200_ref1","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1177\/0142331218804005","article-title":"Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay","volume":"41","author":"Akbari","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"2020121601135066200_ref2","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/S0252-9602(17)30008-5","article-title":"Synchronization of master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control","volume":"37","author":"Ali","year":"2017","journal-title":"Acta Math. Sci. (Chinese)"},{"key":"2020121601135066200_ref3","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1215\/S0012-7094-56-02343-2","article-title":"Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformations","volume":"23","author":"Amir-Mo\u00e9z","year":"1956","journal-title":"Duke Math. J."},{"key":"2020121601135066200_ref4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.physrep.2008.09.002","article-title":"Synchronization in complex networks","volume":"469","author":"Arenas","year":"2008","journal-title":"Phys. Rep."},{"key":"2020121601135066200_ref5","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.neunet.2016.05.003","article-title":"Synchronization of fractional-order complex-valued neural networks with time delay","volume":"81","author":"Bao","year":"2016","journal-title":"Neural Netw."},{"key":"2020121601135066200_ref6","doi-asserted-by":"crossref","first-page":"1398","DOI":"10.1109\/TIE.2006.881997","article-title":"Overview of control and grid synchronization for distributed power generation systems","volume":"53","author":"Blaabjerg","year":"2006","journal-title":"IEEE Trans. Ind. Electron."},{"key":"2020121601135066200_ref7","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1109\/81.989169","article-title":"Generalized state-space observers for chaotic synchronization and secure communication","volume":"49","author":"Boutayeb","year":"2002","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"2020121601135066200_ref8","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.neucom.2013.12.039","article-title":"Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control","volume":"133","author":"Chandrasekar","year":"2014","journal-title":"Neurocomputing"},{"key":"2020121601135066200_ref9","first-page":"508","article-title":"A secure communication scheme based on the phase synchronization of chaotic systems. Chaos","volume":"13","author":"Chen","year":"2003"},{"key":"2020121601135066200_ref10","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1049\/iet-ipr.2012.0660","article-title":"Combining fractional-order edge detection and chaos synchronization classifier for fingerprint identification","volume":"8","author":"Chen","year":"2014","journal-title":"IET Image Process."},{"key":"2020121601135066200_ref11","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.1073\/pnas.1212134110","article-title":"Synchronization in complex oscillator networks and smart grids","volume":"110","author":"D\u00f6rfler","year":"2013","journal-title":"Proc. Natl. Acad. Sci. U.S. A."},{"key":"2020121601135066200_ref12","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1002\/rnc.3602","article-title":"Stochastic stability and stabilization of a class of piecewise-homogeneous Markov jump linear systems with mixed uncertainties","volume":"27","author":"Faraji-Niri","year":"2017","journal-title":"Int. J. Robust Nonlin."},{"key":"2020121601135066200_ref13","doi-asserted-by":"crossref","first-page":"37","DOI":"10.5755\/j01.itc.46.1.13881","article-title":"Stochastic stability and stabilization of semi-Markov jump linear systems with uncertain transition rates","volume":"46","author":"Faraji-Niri","year":"2017","journal-title":"ITC"},{"issue":"S1","key":"2020121601135066200_ref14","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1002\/cplx.21745","article-title":"Stabilization of active fault-tolerant control systems by uncertain nonhomogeneous Markovian jump models","volume":"21","author":"Faraji-Niri","year":"2016","journal-title":"Complexity"},{"key":"2020121601135066200_ref15","doi-asserted-by":"crossref","first-page":"4234","DOI":"10.1007\/s00034-018-0767-y","article-title":"Robust non-fragile asynchronous controller design for continuous-time Markov jump linear systems: non-homogeneous Markov process approach","volume":"37","author":"Faraji-Niri","year":"2018","journal-title":"Circ. Syst. Signal Pr."},{"key":"2020121601135066200_ref16","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1007\/s11071-016-2711-7","article-title":"Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control","volume":"85","author":"Feng","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"2020121601135066200_ref17","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1002\/rnc.2807","article-title":"Discrete-time output feedback for Markov jump systems with uncertain transition probabilities","volume":"23","author":"Fioravanti","year":"2013","journal-title":"Int. J. Robust Nonlin."},{"key":"2020121601135066200_ref19","doi-asserted-by":"crossref","first-page":"8934","DOI":"10.1016\/j.jfranklin.2018.10.005","article-title":"Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control","volume":"335","author":"Gyurkovics","year":"2018","journal-title":"J. Franklin Inst. B"},{"key":"2020121601135066200_ref20","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1002\/cplx.21472","article-title":"Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties","volume":"19","author":"He","year":"2014","journal-title":"Complexity"},{"key":"2020121601135066200_ref21","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1002\/asjc.1910","article-title":"Synchronization of complex dynamical networks with dynamical behavior links","volume":"22","author":"Kazemy","year":"2018","journal-title":"Asian J. Control"},{"key":"2020121601135066200_ref22","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1007\/s00521-016-2661-5","article-title":"Global synchronization of neural networks with hybrid coupling: a delay interval segmentation approach","volume":"30","author":"Kazemy","year":"2018","journal-title":"Neural Comput. Appl."},{"key":"2020121601135066200_ref23","doi-asserted-by":"crossref","first-page":"2656","DOI":"10.1007\/s12555-017-0718-6","article-title":"Consecutive synchronization of a delayed complex dynamical network via distributed adaptive control approach","volume":"16","author":"Kazemy","year":"2018","journal-title":"Int. J. Control Autom. Syst."},{"key":"2020121601135066200_ref24","first-page":"286","article-title":"Delay-dependent robust absolute stability criteria for uncertain multiple time-delayed Lur\u2019e systems","volume":"227","author":"Kazemy","year":"2013","journal-title":"Proc. Inst. Mech. Eng. Pt. I: J. Syst. Contr. Eng."},{"key":"2020121601135066200_ref25","doi-asserted-by":"crossref","first-page":"2623","DOI":"10.1177\/0142331218805533","article-title":"Sliding mode synchronization of a delayed complex dynamical network in the presence of uncertainties and external disturbances","volume":"41","author":"Kazemy","year":"2019","journal-title":"T. I. Meas. Control"},{"key":"2020121601135066200_ref26","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1109\/TCSI.2009.2023937","article-title":"Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint","volume":"57","author":"Li","year":"2010","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"2020121601135066200_ref27","doi-asserted-by":"crossref","DOI":"10.1088\/1751-8113\/43\/10\/105101","article-title":"Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays","volume":"43","author":"Li","year":"2010","journal-title":"J. Phys. A Math. Theor."},{"key":"2020121601135066200_ref28","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s11071-013-0949-x","article-title":"Synchronization of complex networks with nonhomogeneous Markov jump topology","volume":"74","author":"Li","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"2020121601135066200_ref29","doi-asserted-by":"crossref","first-page":"2967","DOI":"10.1109\/TCSI.2010.2052508","article-title":"Exponential synchronization of complex delayed dynamical networks with switching topology","volume":"57","author":"Liu","year":"2010","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"2020121601135066200_ref30","doi-asserted-by":"crossref","first-page":"6045","DOI":"10.1016\/j.jfranklin.2018.06.006","article-title":"Group controllability of two-time-scale multi-agent networks","volume":"355","author":"Long","year":"2018","journal-title":"J. Franklin Inst. B"},{"key":"2020121601135066200_ref31","first-page":"299","article-title":"Second-order controllability of two-time-scale multi-agent systems","volume":"343","author":"Long","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"2020121601135066200_ref32","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1016\/j.apm.2012.06.003","article-title":"Adaptive synchronization of two coupled chaotic Hindmarsh-rose neurons by controlling the membrane potential of a slave neuron","volume":"37","author":"Hong","year":"2013","journal-title":"Appl. Math. Model."},{"key":"2020121601135066200_ref33","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1016\/j.physa.2013.01.023","article-title":"The power grid as a complex network: a survey","volume":"392","author":"Pagani","year":"2013","journal-title":"Physica A"},{"key":"2020121601135066200_ref34","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 J. IFAC"},{"key":"2020121601135066200_ref35","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00034-014-9854-x","article-title":"Stochastic sampled-data control for exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay","volume":"34","author":"Rakkiyappan","year":"2015","journal-title":"Circ. Syst. Signal Pr."},{"key":"2020121601135066200_ref36","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.cnsns.2014.12.004","article-title":"Finite-time ${H}\\_{\\infty } $ synchronization for complex networks with semi-Markov jump topology","volume":"24","author":"Shen","year":"2015","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2020121601135066200_ref37","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1038\/35065725","article-title":"Exploring complex networks","volume":"410","author":"Strogatz","year":"2001","journal-title":"Nature"},{"key":"2020121601135066200_ref38","doi-asserted-by":"crossref","first-page":"2860","DOI":"10.1016\/j.automatica.2013.05.030","article-title":"Wirtinger-based integral inequality: application to time-delay systems","volume":"49","author":"Seuret","year":"2013","journal-title":"Automatica J. IFAC"},{"key":"2020121601135066200_ref39","volume-title":"Delay-dependent reciprocally convex combination lemma.","author":"Seuret","year":"2016"},{"key":"2020121601135066200_ref40","first-page":"1","article-title":"Finite-time control for Markovian jump systems with polytopic uncertain transition description and actuator saturation","volume":"2014","author":"Tang","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"2020121601135066200_ref41","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1002\/cplx.21647","article-title":"Mean square exponential synchronization for impulsive coupled neural networks with time-varying delays and stochastic disturbances","volume":"21","author":"Tang","year":"2016","journal-title":"Complexity"},{"key":"2020121601135066200_ref42","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0951-8320(95)00149-2","article-title":"Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function","volume":"52","author":"Xie","year":"1996","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"2020121601135066200_ref43","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1016\/j.automatica.2007.09.016","article-title":"${H}\\_{\\infty } $ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities","volume":"44","author":"Wang","year":"2008","journal-title":"Automatica J. IFAC"},{"key":"2020121601135066200_ref44","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1109\/TNNLS.2015.2423853","article-title":"Pinning control strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms","volume":"27","author":"Wang","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2020121601135066200_ref45","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.neucom.2014.04.036","article-title":"Mean square exponential synchronization for a class of Markovian switching complex networks under feedback control and M-matrix approach","volume":"144","author":"Wang","year":"2014","journal-title":"Neurocomputing"},{"key":"2020121601135066200_ref46","doi-asserted-by":"crossref","first-page":"2136","DOI":"10.1016\/j.jfranklin.2012.03.005","article-title":"Stochastic stability analysis of piecewise homogeneous Markovian jump neural networks with mixed time-delays","volume":"349","author":"Wu","year":"2012","journal-title":"J. Franklin Inst. B"},{"key":"2020121601135066200_ref47","doi-asserted-by":"crossref","first-page":"2768","DOI":"10.1109\/TAC.2015.2404271","article-title":"Free-matrix-based integral inequality for stability analysis of systems with time-varying delay","volume":"60","author":"Zeng","year":"2015","journal-title":"IEEE Trans. Automat. Contr."},{"key":"2020121601135066200_ref48","doi-asserted-by":"crossref","first-page":"2502","DOI":"10.1016\/j.automatica.2009.07.013","article-title":"Synchronization of complex dynamical networks with switching topology: a switched system point of view","volume":"45","author":"Zhao","year":"2009","journal-title":"Automatica J. IFAC"},{"key":"2020121601135066200_ref49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1049\/iet-cta.2018.5188","article-title":"Overview of recent advances in stability of linear systems with time-varying delays","volume":"13","author":"Zhang","year":"2019","journal-title":"IET Control Theory Appl."},{"key":"2020121601135066200_ref50","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.automatica.2017.04.048","article-title":"An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay","volume":"84","author":"Zhang","year":"2017","journal-title":"Automatica J. IFAC"},{"key":"2020121601135066200_ref51","doi-asserted-by":"crossref","first-page":"5319","DOI":"10.1109\/TNNLS.2018.2797279","article-title":"Admissible delay upper bounds for global asymptotic stability of neural networks with time-varying delays","volume":"29","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2020121601135066200_ref52","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.neucom.2018.06.038","article-title":"An overview of recent developments in Lyapunov-Krasovskii functionals and stability criteria for recurrent neural networks with time-varying delays","volume":"313","author":"Zhang","year":"2018","journal-title":"Neurocomputing"},{"key":"2020121601135066200_ref53","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1007\/s12555-012-9511-8","article-title":"Adaptive target synchronization for wireless sensor networks with Markov delays and noise perturbation","volume":"11","author":"Zhou","year":"2013","journal-title":"Int. J. Control. Autom. Syst."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/4\/1168\/34912243\/dnz041.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/4\/1168\/34912243\/dnz041.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T06:14:19Z","timestamp":1608099259000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/37\/4\/1168\/5804822"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,7]]},"references-count":52,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4,7]]},"published-print":{"date-parts":[[2020,12,16]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnz041","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"value":"0265-0754","type":"print"},{"value":"1471-6887","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,12]]},"published":{"date-parts":[[2020,4,7]]}}}