{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T14:23:08Z","timestamp":1773843788120,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s00498-022-00340-3","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T13:32:50Z","timestamp":1672839170000},"page":"307-326","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Controllability of networked systems with heterogeneous dynamics"],"prefix":"10.1007","volume":"35","author":[{"given":"Abhijith","family":"Ajayakumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raju K.","family":"George","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,4]]},"reference":[{"key":"340_CR1","doi-asserted-by":"crossref","unstructured":"Aguilar CO, Gharesifard B (2014) A graph-theoretic classification for the controllability of the Laplacian leader-follower dynamics. In: 53rd IEEE conference on decision and control, pp 619\u2013624","DOI":"10.1109\/CDC.2014.7039450"},{"key":"340_CR2","doi-asserted-by":"publisher","DOI":"10.1109\/TCNS.2022.3203794","author":"A Ajayakumar","year":"2022","unstructured":"Ajayakumar A, George RK (2022) A note on controllability of directed networked system with heterogeneous dynamics. IEEE Trans Control Netw Syst. https:\/\/doi.org\/10.1109\/TCNS.2022.3203794","journal-title":"IEEE Trans Control Netw Syst"},{"issue":"3","key":"340_CR3","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1038\/nn.4502","volume":"20","author":"DS Bassett","year":"2017","unstructured":"Bassett DS, Sporns O (2017) Network neuroscience. Nat Neurosci 20(3):353\u2013364","journal-title":"Nat Neurosci"},{"issue":"19","key":"340_CR4","doi-asserted-by":"publisher","first-page":"245","DOI":"10.3182\/20100913-2-FR-4014.00079","volume":"43","author":"L Blackhall","year":"2010","unstructured":"Blackhall L, Hill DJ (2010) On the structural controllability of networks of linear systems. IFAC Proc Vol 43(19):245\u2013250","journal-title":"IFAC Proc Vol"},{"issue":"2","key":"340_CR5","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/TCS.1975.1084015","volume":"22","author":"F Callier","year":"1975","unstructured":"Callier F, Nahum C (1975) Necessary and sufficient conditions for the complete controllability and observability of systems in series using the co-prime factorization of a rational matrix. IEEE Trans Circuits Syst 22(2):90\u201395","journal-title":"IEEE Trans Circuits Syst"},{"key":"340_CR6","doi-asserted-by":"crossref","unstructured":"Chapman A, Mesbahi M (2013) On strong structural controllability of networked systems: a constrained matching approach. In: 2013 American control conference, pp 6126\u20136131","DOI":"10.1109\/ACC.2013.6580798"},{"issue":"1","key":"340_CR7","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MPE.2009.934876","volume":"8","author":"H Farhangi","year":"2009","unstructured":"Farhangi H (2009) The path of the smart grid. IEEE Power Energy Mag 8(1):18\u201328","journal-title":"IEEE Power Energy Mag"},{"issue":"1","key":"340_CR8","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1109\/TCS.1975.1083955","volume":"22","author":"P Fuhrmann","year":"1975","unstructured":"Fuhrmann P (1975) On controllability and observability of systems connected in parallel. IEEE Trans Circuits Syst 22(1):57\u201357","journal-title":"IEEE Trans Circuits Syst"},{"issue":"1","key":"340_CR9","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1137\/0301009","volume":"12","author":"EG Gilbert","year":"1963","unstructured":"Gilbert EG (1963) Controllability and observability in multivariable control systems. J Soc Ind Appl Math Ser A Control 12(1):128\u2013151","journal-title":"J Soc Ind Appl Math Ser A Control"},{"issue":"4","key":"340_CR10","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1109\/TAC.1976.1101257","volume":"21","author":"K Glover","year":"1976","unstructured":"Glover K, Silverman L (1976) Characterization of structural controllability. IEEE Trans Autom Control 21(4):534\u2013537","journal-title":"IEEE Trans Autom Control"},{"issue":"5","key":"340_CR11","doi-asserted-by":"publisher","first-page":"1778","DOI":"10.1002\/rnc.3986","volume":"28","author":"Y Hao","year":"1976","unstructured":"Hao Y, Duan Z, Chen G (1976) Further on the controllability of networked MIMO LTI systems. Int J Robust Nonlinear Control 28(5):1778\u20131788","journal-title":"Int J Robust Nonlinear Control"},{"issue":"10","key":"340_CR12","doi-asserted-by":"publisher","first-page":"4223","DOI":"10.1109\/TAC.2019.2893899","volume":"64","author":"Y Hao","year":"2019","unstructured":"Hao Y, Duan Z, Chen G, Wu F (2019) New controllability conditions for networked, identical LTI systems. IEEE Trans Autom Control 64(10):4223\u20134228","journal-title":"IEEE Trans Autom Control"},{"issue":"5","key":"340_CR13","doi-asserted-by":"publisher","first-page":"299","DOI":"10.9746\/jcmsi.2.299","volume":"2","author":"S Hara","year":"2009","unstructured":"Hara S, Hayakawa T, Sugata H (2009) LTI systems with generalized frequency variables: a unified framework for homogeneous multi-agent dynamical systems. SICE J Control Meas Syst Integr 2(5):299\u2013306","journal-title":"SICE J Control Meas Syst Integr"},{"issue":"5","key":"340_CR14","first-page":"443","volume":"72","author":"MLJ Hautus","year":"1969","unstructured":"Hautus MLJ (1969) Controllability and observability conditions of linear autonomous systems. Indagationes Mathematicae (Proc) 72(5):443\u2013448","journal-title":"Indagationes Mathematicae (Proc)"},{"key":"340_CR15","volume-title":"Topics in matrix analysis","author":"RA Horn","year":"1994","unstructured":"Horn RA, Johnson CR (1994) Topics in matrix analysis. Cambridge University Press, Cambridge"},{"key":"340_CR16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020411","volume-title":"Matrix analysis","author":"RA Horn","year":"2012","unstructured":"Horn RA, Johnson CR (2012) Matrix analysis. Cambridge University Press, Cambridge"},{"key":"340_CR17","doi-asserted-by":"crossref","unstructured":"Jarczyk JC, Svaricek F, Alt B (2011) Strong structural controllability of linear systems revisited. In: 2011 50th IEEE conference on decision and control and european control conference, pp 1213\u20131218","DOI":"10.1109\/CDC.2011.6160392"},{"key":"340_CR18","doi-asserted-by":"crossref","unstructured":"Ji M, Egerstedt M (2007) A graph-theoretic characterization of controllability for multi-agent systems. In: 2007 American control conference, pp 4588\u20134593","DOI":"10.1109\/ACC.2007.4283010"},{"issue":"1\u20132","key":"340_CR19","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1080\/01630568908816296","volume":"10","author":"MC Joshi","year":"1989","unstructured":"Joshi MC, George RK (1989) Controllability of nonlinear systems. Numer Funct Anal Optim 10(1\u20132):139\u2013166","journal-title":"Numer Funct Anal Optim"},{"key":"340_CR20","doi-asserted-by":"crossref","unstructured":"Kalman RE (1960) On the general theory of control systems. In: Proceedings first international conference on automatic control, Moscow, USSR, pp 481\u2013492","DOI":"10.1016\/S1474-6670(17)70094-8"},{"issue":"4","key":"340_CR21","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1073\/pnas.48.4.596","volume":"48","author":"RE Kalman","year":"1962","unstructured":"Kalman RE (1962) Canonical structure of linear dynamical systems. Proc Natl Acad Sci USA 48(4):596","journal-title":"Proc Natl Acad Sci USA"},{"issue":"3","key":"340_CR22","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1109\/TAC.1974.1100557","volume":"19","author":"CT Lin","year":"1974","unstructured":"Lin CT (1974) Structural controllability. IEEE Trans Autom Control 19(3):201\u2013208","journal-title":"IEEE Trans Autom Control"},{"issue":"2","key":"340_CR23","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1080\/00207179.2012.723136","volume":"86","author":"X Liu","year":"2013","unstructured":"Liu X, Lin H, Chen BM (2013) Graph-theoretic characterisations of structural controllability for multi-agent system with switching topology. Int J Control 86(2):222\u2013231","journal-title":"Int J Control"},{"issue":"3","key":"340_CR24","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1109\/TAC.1981.1102707","volume":"26","author":"H Mayeda","year":"1981","unstructured":"Mayeda H (1981) On structural controllability theorem. IEEE Trans Autom Control 26(3):795\u2013798","journal-title":"IEEE Trans Autom Control"},{"issue":"3","key":"340_CR25","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1002\/asjc.2528","volume":"24","author":"J Mu","year":"2022","unstructured":"Mu J, Wu J, Li N, Zhang X, Li S (2022) Structural controllability of networked systems with general heterogeneous subsystems. Asian J Control 24(3):1321\u20131332","journal-title":"Asian J Control"},{"key":"340_CR26","unstructured":"Muni VS, Muhammed Rafeek KV, Reddy GJ, George RK (2022) On the selection of leaders for the controllability of multi-agent networks. Bull Iran Math Soc 1\u201343 (2022)"},{"issue":"7369","key":"340_CR27","first-page":"E4","volume":"478","author":"FJ M\u00fcller","year":"1981","unstructured":"M\u00fcller FJ, Schuppert A (1981) Few inputs can reprogram biological networks. IEEE Trans Autom Control 478(7369):E4\u2013E4","journal-title":"IEEE Trans Autom Control"},{"issue":"7","key":"340_CR28","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1038\/nphys2327","volume":"8","author":"T Nepusz","year":"2012","unstructured":"Nepusz T, Vicsek T (2012) Controlling edge dynamics in complex networks. Nat Phys 8(7):568\u2013573","journal-title":"Nat Phys"},{"issue":"1","key":"340_CR29","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1137\/060674909","volume":"48","author":"A Rahmani","year":"2009","unstructured":"Rahmani A, Ji M, Mesbahi M, Egerstedt M (2009) Controllability of multi-agent systems from a graph-theoretic perspective. SIAM J Control Optim 48(1):162\u2013186","journal-title":"SIAM J Control Optim"},{"key":"340_CR30","volume-title":"Linear system theory","author":"WJ Rugh","year":"1996","unstructured":"Rugh WJ (1996) Linear system theory. Prentice-Hall, Hoboken"},{"key":"340_CR31","doi-asserted-by":"crossref","unstructured":"Tanner HG (2004) On the controllability of nearest neighbour interconnections. In: 2004 43rd IEEE conference on decision and control (CDC) (IEEE Cat. No. 04CH37601), vol 3, pp 2467\u20132472","DOI":"10.1109\/CDC.2004.1428782"},{"key":"340_CR32","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.automatica.2016.03.013","volume":"69","author":"L Wang","year":"2016","unstructured":"Wang L, Chen G, Wang X, Tang WKS (2016) Controllability of networked MIMO systems. Automatica 69:405\u2013409","journal-title":"Automatica"},{"issue":"2088","key":"340_CR33","doi-asserted-by":"publisher","first-page":"20160215","DOI":"10.1098\/rsta.2016.0215","volume":"375","author":"L Wang","year":"2017","unstructured":"Wang L, Wang X, Chen G (2017) Controllability of networked higher-dimensional systems with one-dimensional communication. Philos Trans R Soc A Math Phys Eng Sci 375(2088):20160215","journal-title":"Philos Trans R Soc A Math Phys Eng Sci"},{"key":"340_CR34","doi-asserted-by":"crossref","unstructured":"Wang P, Xiang L, Chen F (2017) Controllability of heterogeneous networked MIMO systems. In: International workshop on complex systems and networks (IWCSN), pp 45\u201349","DOI":"10.1109\/IWCSN.2017.8276502"},{"issue":"2","key":"340_CR35","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1109\/MCAS.2019.2909446","volume":"19","author":"L Xiang","year":"2017","unstructured":"Xiang L, Chen F, Ren W, Chen G (2017) Advances in network controllability. IEEE Circuits Syst Mag 19(2):8\u201332","journal-title":"IEEE Circuits Syst Mag"},{"key":"340_CR36","doi-asserted-by":"crossref","unstructured":"Xiang L, Wang P, Chen F, Chen G (2019) Controllability of directed networked MIMO systems with heterogeneous dynamics. IEEE Trans Control Netw Syst","DOI":"10.1109\/TCNS.2019.2948994"},{"issue":"3","key":"340_CR37","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.ifacol.2019.06.005","volume":"52","author":"M Xue","year":"2019","unstructured":"Xue M, Roy S (2019) Structural controllability of linear dynamical networks with homogeneous subsystems. IFAC-PapersOnLine 52(3):25\u201330","journal-title":"IFAC-PapersOnLine"},{"issue":"12","key":"340_CR38","doi-asserted-by":"publisher","first-page":"4125","DOI":"10.1109\/TAC.2016.2546180","volume":"61","author":"AY Yaz\u0131c\u0131o\u011flu","year":"2016","unstructured":"Yaz\u0131c\u0131o\u011flu AY, Abbas W, Egerstedt M (2016) Graph distances and controllability of networks. IEEE Trans Autom Control 61(12):4125\u20134130","journal-title":"IEEE Trans Autom Control"},{"key":"340_CR39","doi-asserted-by":"crossref","unstructured":"Zamani M, Lin H (2009) Structural controllability of multi-agent systems. In: 2009 American control conference, pp 5743\u20135748","DOI":"10.1109\/ACC.2009.5160170"},{"issue":"7","key":"340_CR40","doi-asserted-by":"publisher","first-page":"3408","DOI":"10.1109\/TAC.2016.2612831","volume":"69","author":"Y Zhang","year":"2017","unstructured":"Zhang Y, Zhou T (2017) Controllability analysis for a networked dynamic system with autonomous subsystems. IEEE Trans Autom Control 69(7):3408\u20133415","journal-title":"IEEE Trans Autom Control"},{"key":"340_CR41","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.4772","author":"B Zhao","year":"2019","unstructured":"Zhao B, Chen MZQ, Guan Y, Wang L (2019) Controllability of heterogeneous multiagent systems. Int J Robust Nonlinear Control. https:\/\/doi.org\/10.1002\/rnc.4772","journal-title":"Int J Robust Nonlinear Control"},{"key":"340_CR42","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.automatica.2014.10.121","volume":"52","author":"T Zhou","year":"2015","unstructured":"Zhou T (2015) On the controllability and observability of networked dynamic systems. Automatica 52:63\u201375","journal-title":"Automatica"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-022-00340-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00498-022-00340-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-022-00340-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T04:04:55Z","timestamp":1684469095000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00498-022-00340-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,4]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["340"],"URL":"https:\/\/doi.org\/10.1007\/s00498-022-00340-3","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,4]]},"assertion":[{"value":"22 June 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2023","order":3,"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 there is no potential conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}