{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T07:55:30Z","timestamp":1775289330592,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T00:00:00Z","timestamp":1543449600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"crossref","award":["1355845"],"award-info":[{"award-number":["1355845"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"name":"European Research Council","award":["670645"],"award-info":[{"award-number":["670645"]}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["670645"],"award-info":[{"award-number":["670645"]}],"id":[{"id":"10.13039\/501100000781","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":[[2018,12]]},"DOI":"10.1007\/s00498-018-0229-x","type":"journal-article","created":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T01:11:46Z","timestamp":1543453906000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Monotonicity on homogeneous spaces"],"prefix":"10.1007","volume":"30","author":[{"given":"Cyrus","family":"Mostajeran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodolphe","family":"Sepulchre","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,11,29]]},"reference":[{"key":"229_CR1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244","volume-title":"Optimization algorithms on matrix manifolds","author":"P Absil","year":"2008","unstructured":"Absil P, Mahony R, Sepulchre R (2008) Optimization algorithms on matrix manifolds. Princeton University Press, Princeton"},{"key":"229_CR2","doi-asserted-by":"publisher","unstructured":"Altafini C (2016) Minimal eventually positive realizations of externally positive systems. Automatica 68:140\u2013147. https:\/\/doi.org\/10.1016\/j.automatica.2016.01.072 , http:\/\/www.sciencedirect.com\/science\/article\/pii\/S000510981630019X","DOI":"10.1016\/j.automatica.2016.01.072"},{"issue":"2","key":"229_CR3","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1109\/81.486435","volume":"43","author":"BDO Anderson","year":"1996","unstructured":"Anderson BDO, Deistler M, Farina L, Benvenuti L (1996) Nonnegative realization of a linear system with nonnegative impulse response. IEEE Trans Circuits Syst I Fundam Theory Appl 43(2):134\u2013142. https:\/\/doi.org\/10.1109\/81.486435","journal-title":"IEEE Trans Circuits Syst I Fundam Theory Appl"},{"issue":"10","key":"229_CR4","doi-asserted-by":"publisher","first-page":"1684","DOI":"10.1109\/TAC.2003.817920","volume":"48","author":"D Angeli","year":"2003","unstructured":"Angeli D, Sontag ED (2003) Monotone control systems. IEEE Trans Autom Control 48(10):1684\u20131698","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"229_CR5","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.nonrwa.2006.09.006","volume":"9","author":"D Angeli","year":"2008","unstructured":"Angeli D, Sontag ED (2008) Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles. Nonlinear Anal Real World Appl 9(1):128\u2013140","journal-title":"Nonlinear Anal Real World Appl"},{"key":"229_CR6","doi-asserted-by":"crossref","unstructured":"Angeli D, Sontag ED (2012) Remarks on the invalidation of biological models using monotone systems theory. In: 2012 IEEE 51st IEEE conference on decision and control CDC, pp 2989\u20132994","DOI":"10.1109\/CDC.2012.6426795"},{"issue":"7","key":"229_CR7","doi-asserted-by":"publisher","first-page":"1822","DOI":"10.1073\/pnas.0308265100","volume":"101","author":"D Angeli","year":"2004","unstructured":"Angeli D, Ferrell JE, Sontag ED (2004) Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc Natl Acad Sci 101(7):1822\u20131827","journal-title":"Proc Natl Acad Sci"},{"key":"229_CR8","doi-asserted-by":"crossref","DOI":"10.1090\/stml\/022","volume-title":"An introduction to Lie groups and the geometry of homogeneous spaces","author":"A Arvanitoge\u014drgos","year":"2003","unstructured":"Arvanitoge\u014drgos A (2003) An introduction to Lie groups and the geometry of homogeneous spaces, vol 22. American Mathematical Society, Providence"},{"key":"229_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74311-8","volume-title":"Einstein manifolds: classics in mathematics","author":"A Besse","year":"1987","unstructured":"Besse A (1987) Einstein manifolds: classics in mathematics. Springer, Berlin"},{"key":"229_CR10","volume-title":"Positive definite matrices","author":"R Bhatia","year":"2007","unstructured":"Bhatia R (2007) Positive definite matrices. Princeton University Press, Princeton"},{"issue":"3","key":"229_CR11","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/s10910-006-9075-z","volume":"41","author":"P Leenheer De","year":"2007","unstructured":"De Leenheer P, Angeli D, Sontag ED (2007) Monotone chemical reaction networks. J Math Chem 41(3):295\u2013314","journal-title":"J Math Chem"},{"issue":"2","key":"229_CR12","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A Edelman","year":"1999","unstructured":"Edelman A, Arias TA, Smith ST (1999) The geometry of algorithms with orthogonality constraints. SIAM J Matrix Anal Appl 20(2):303\u2013353","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"2","key":"229_CR13","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.sysconle.2004.08.003","volume":"54","author":"G Enciso","year":"2005","unstructured":"Enciso G, Sontag ED (2005) Monotone systems under positive feedback: multistability and a reduction theorem. Syst Control Lett 54(2):159\u2013168","journal-title":"Syst Control Lett"},{"key":"229_CR14","doi-asserted-by":"publisher","DOI":"10.1002\/9781118033029","volume-title":"Positive linear systems: theory and applications. Pure and applied mathematics","author":"L Farina","year":"2000","unstructured":"Farina L, Rinaldi S (2000) Positive linear systems: theory and applications. Pure and applied mathematics. Wiley, New York"},{"key":"229_CR15","doi-asserted-by":"crossref","unstructured":"Forni F (2015) Differential positivity on compact sets. In: 2015 54th IEEE conference on decision and control (CDC), pp 6355\u20136360","DOI":"10.1109\/CDC.2015.7403220"},{"key":"229_CR16","doi-asserted-by":"crossref","unstructured":"Forni F, Sepulchre R (2014) Differential analysis of nonlinear systems: revisiting the pendulum example. In: 53rd IEEE conference of decision and control, Los Angeles","DOI":"10.1109\/CDC.2014.7039987"},{"issue":"2","key":"229_CR17","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1109\/TAC.2015.2437523","volume":"61","author":"F Forni","year":"2016","unstructured":"Forni F, Sepulchre R (2016) Differentially positive systems. IEEE Trans Autom Control 61(2):346\u2013359. https:\/\/doi.org\/10.1109\/TAC.2015.2437523","journal-title":"IEEE Trans Autom Control"},{"key":"229_CR18","doi-asserted-by":"publisher","unstructured":"Forni F, Sepulchre R (2018) Differential dissipativity theory for dominance analysis. IEEE Trans Autom Control. https:\/\/doi.org\/10.1109\/TAC.2018.2867920","DOI":"10.1109\/TAC.2018.2867920"},{"key":"229_CR19","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/BF01764120","volume":"160","author":"G Fusco","year":"1991","unstructured":"Fusco G, Oliva W (1991) A Perron theorem for the existence of invariant subspaces. WM Annali di Matematica pura ed applicata 160:63\u201376","journal-title":"WM Annali di Matematica pura ed applicata"},{"issue":"2","key":"229_CR20","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1080\/10618600.1999.10474808","volume":"8","author":"CR Goodall","year":"1999","unstructured":"Goodall CR, Mardia KV (1999) Projective shape analysis. J Comput Gr Stat 8(2):143\u2013168","journal-title":"J Comput Gr Stat"},{"key":"229_CR21","doi-asserted-by":"publisher","unstructured":"Grussler C, Rantzer A (2014) Modified balanced truncation preserving ellipsoidal cone-invariance. In: 53rd IEEE conference on decision and control, pp 2365\u20132370. https:\/\/doi.org\/10.1109\/CDC.2014.7039749","DOI":"10.1109\/CDC.2014.7039749"},{"key":"229_CR22","unstructured":"Grussler C, Sepulchre R (2018) Strongly unimodal systems. arXiv preprint arXiv:181103986"},{"key":"229_CR23","doi-asserted-by":"publisher","unstructured":"Grussler C, Umenberger J, Manchester IR (2017) Identification of externally positive systems. In: 2017 IEEE 56th annual conference on decision and control (CDC), pp 6549\u20136554. https:\/\/doi.org\/10.1109\/CDC.2017.8264646","DOI":"10.1109\/CDC.2017.8264646"},{"key":"229_CR24","volume-title":"Lie semigroups and their applications","author":"J Hilgert","year":"2006","unstructured":"Hilgert J, Neeb KH (2006) Lie semigroups and their applications. Springer, Berlin"},{"key":"229_CR25","volume-title":"Lie groups, convex cones, and semi-groups","author":"J Hilgert","year":"1989","unstructured":"Hilgert J, Hofmann KH, Lawson J (1989) Lie groups, convex cones, and semi-groups. Oxford University Press, Oxford"},{"key":"229_CR26","first-page":"1","volume":"383","author":"MW Hirsch","year":"1988","unstructured":"Hirsch MW (1988) Stability and convergence in strongly monotone dynamical systems. Journal f\u00fcr die reine und angewandte Mathematik 383:1\u201353","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"issue":"6","key":"229_CR27","doi-asserted-by":"publisher","first-page":"988","DOI":"10.1109\/TAC.2003.812781","volume":"48","author":"A Jadbabaie","year":"2003","unstructured":"Jadbabaie A, Lin J (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988\u20131001","journal-title":"IEEE Trans Autom Control"},{"issue":"10","key":"229_CR28","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1080\/00029890.1972.11993188","volume":"79","author":"SL Kleiman","year":"1972","unstructured":"Kleiman SL, Laksov D (1972) Schubert calculus. Am Math Mon 79(10):1061\u20131082","journal-title":"Am Math Mon"},{"key":"229_CR29","volume-title":"Fundamentals of differential geometry","author":"S Lang","year":"2012","unstructured":"Lang S (2012) Fundamentals of differential geometry, vol 191. Springer, Berlin"},{"key":"229_CR30","first-page":"163","volume":"1","author":"JD Lawson","year":"1991","unstructured":"Lawson JD (1991) Polar and Ol\u2019shanski decompositions. Semin Sophus Lie 1:163\u2013173","journal-title":"Semin Sophus Lie"},{"key":"229_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21752-9","volume-title":"Introduction to smooth manifolds. Graduate texts in mathematics","author":"JM Lee","year":"2003","unstructured":"Lee JM (2003) Introduction to smooth manifolds. Graduate texts in mathematics. Springer, New York"},{"key":"229_CR32","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01170633","volume":"38","author":"K L\u00f6wner","year":"1934","unstructured":"L\u00f6wner K (1934) \u00dcber monotone matrixfunktionen. Mathematische Zeitschrift 38:177\u2013216","journal-title":"Mathematische Zeitschrift"},{"key":"229_CR33","volume-title":"Introduction to dynamic systems: theory, models, and applications","author":"DG Luenberger","year":"1979","unstructured":"Luenberger DG (1979) Introduction to dynamic systems: theory, models, and applications, vol 1. Wiley, New York"},{"key":"229_CR34","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/j.automatica.2016.07.026","volume":"74","author":"JM Montenbruck","year":"2016","unstructured":"Montenbruck JM, Allg\u00f6wer F (2016) Asymptotic stabilization of submanifolds embedded in riemannian manifolds. Automatica 74:349\u2013359","journal-title":"Automatica"},{"key":"229_CR35","doi-asserted-by":"crossref","unstructured":"Moreau L (2004) Stability of continuous-time distributed consensus algorithms. In: 43rd IEEE conference on decision and control, vol 4, pp 3998\u20134003","DOI":"10.1109\/CDC.2004.1429377"},{"key":"229_CR36","doi-asserted-by":"crossref","unstructured":"Mostajeran C, Sepulchre R (2016) Invariant differential positivity and consensus on Lie groups. In: 10th IFAC symposium on nonlinear control systems","DOI":"10.1016\/j.ifacol.2016.10.236"},{"key":"229_CR37","doi-asserted-by":"crossref","unstructured":"Mostajeran C, Sepulchre R (2017) Affine-invariant orders on the set of positive-definite matrices. In: International conference on the geometric science of information. Springer","DOI":"10.1007\/978-3-319-68445-1_71"},{"key":"229_CR38","doi-asserted-by":"crossref","unstructured":"Mostajeran C, Sepulchre R (2017) Differential positivity with respect to cones of rank k. In: IFAC world congress","DOI":"10.1016\/j.ifacol.2017.08.1507"},{"key":"229_CR39","doi-asserted-by":"publisher","unstructured":"Mostajeran C, Sepulchre R (2018) Ordering positive definite matrices. Inf Geom. https:\/\/doi.org\/10.1007\/s41884-018-0003-7","DOI":"10.1007\/s41884-018-0003-7"},{"issue":"3","key":"229_CR40","doi-asserted-by":"publisher","first-page":"2436","DOI":"10.1137\/17M1127168","volume":"56","author":"C Mostajeran","year":"2018","unstructured":"Mostajeran C, Sepulchre R (2018) Positivity, monotonicity, and consensus on Lie groups. SIAM J Control Optim 56(3):2436\u20132461. https:\/\/doi.org\/10.1137\/17M1127168","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"229_CR41","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/BF01245086","volume":"104","author":"KH Neeb","year":"1991","unstructured":"Neeb KH (1991) Conal orders on homogeneous spaces. Invent Math 104(1):467\u2013496","journal-title":"Invent Math"},{"key":"229_CR42","unstructured":"Newhouse S (2004) Cone-fields, domination, and hyperbolicity. In: Brin M, Hasselblatt B, Katok AB, Pesin Y (eds) Modern dynamical systems and applications. Cambridge University Press, pp 419\u2013432"},{"issue":"2","key":"229_CR43","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1137\/0322013","volume":"22","author":"Y Ohta","year":"1984","unstructured":"Ohta Y, Maeda H, Kodama S (1984) Reachability, observability, and realizability of continuous-time positive systems. SIAM J Control Optim 22(2):171\u2013180. https:\/\/doi.org\/10.1137\/0322013","journal-title":"SIAM J Control Optim"},{"issue":"3","key":"229_CR44","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1109\/TAC.2005.864190","volume":"51","author":"R Olfati-Saber","year":"2006","unstructured":"Olfati-Saber R (2006) Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Control 51(3):401\u2013420","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"229_CR45","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1109\/JPROC.2006.887293","volume":"95","author":"R Olfati-Saber","year":"2007","unstructured":"Olfati-Saber R, Fax J, Murray R (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215\u2013233","journal-title":"Proc IEEE"},{"issue":"5","key":"229_CR46","doi-asserted-by":"publisher","first-page":"1978","DOI":"10.1016\/j.jde.2008.10.015","volume":"246","author":"LA Sanchez","year":"2009","unstructured":"Sanchez LA (2009) Cones of rank 2 and the Poincare\u2013Bendixson property for a new class of monotone systems. J Differ Equ 246(5):1978\u20131990","journal-title":"J Differ Equ"},{"issue":"2","key":"229_CR47","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/j.jmaa.2009.08.058","volume":"363","author":"LA Sanchez","year":"2010","unstructured":"Sanchez LA (2010) Existence of periodic orbits for high-dimensional autonomous systems. J Math Anal Appl 363(2):409\u2013418","journal-title":"J Math Anal Appl"},{"issue":"1","key":"229_CR48","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.arcontrol.2011.03.003","volume":"35","author":"R Sepulchre","year":"2011","unstructured":"Sepulchre R (2011) Consensus on nonlinear spaces. Ann Rev Control 35(1):56\u201364","journal-title":"Ann Rev Control"},{"key":"229_CR49","doi-asserted-by":"publisher","unstructured":"Sepulchre R, Sarlette A, Rouchon P (2010) Consensus in non-commutative spaces. In: 49th IEEE conference on decision and control (CDC), pp 6596\u20136601. https:\/\/doi.org\/10.1109\/CDC.2010.5717072","DOI":"10.1109\/CDC.2010.5717072"},{"key":"229_CR50","volume-title":"Monotone dynamical systems","author":"HL Smith","year":"1995","unstructured":"Smith HL (1995) Monotone dynamical systems. AMS, Providence"},{"key":"229_CR51","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/041","volume-title":"Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems","author":"HL Smith","year":"2008","unstructured":"Smith HL (2008) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, vol 41. American Mathematical Society, Providence"},{"issue":"4","key":"229_CR52","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1137\/S0036139902406905","volume":"63","author":"HL Smith","year":"2003","unstructured":"Smith HL, De Leenheer P (2003) Virus dynamics: a global analysis. SIAM J Appl Math 63(4):1313\u20131327","journal-title":"SIAM J Appl Math"},{"issue":"5","key":"229_CR53","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1109\/TSP.2005.845428","volume":"53","author":"ST Smith","year":"2005","unstructured":"Smith ST (2005) Covariance, subspace, and intrinsic Cramer\u2013Rao bounds. IEEE Trans Signal Process 53(5):1610\u20131630. https:\/\/doi.org\/10.1109\/TSP.2005.845428","journal-title":"IEEE Trans Signal Process"},{"key":"229_CR54","doi-asserted-by":"crossref","unstructured":"Turaga P, Veeraraghavan A, Chellappa R (2008) Statistical analysis on stiefel and grassmann manifolds with applications in computer vision. In: IEEE conference on computer vision and pattern recognition, 2008\u2014CVPR 2008. IEEE, pp 1\u20138","DOI":"10.1109\/CVPR.2008.4587733"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00498-018-0229-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-018-0229-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-018-0229-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T07:03:21Z","timestamp":1775286201000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00498-018-0229-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,29]]},"references-count":54,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["229"],"URL":"https:\/\/doi.org\/10.1007\/s00498-018-0229-x","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,29]]},"assertion":[{"value":"21 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 November 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 November 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"22"}}