{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:35:30Z","timestamp":1775464530649,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,9,1]],"date-time":"2018-09-01T00:00:00Z","timestamp":1535760000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["RE 2917\/5-1"],"award-info":[{"award-number":["RE 2917\/5-1"]}],"id":[{"id":"10.13039\/501100001659","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":[[2018,9]]},"DOI":"10.1007\/s00498-018-0221-5","type":"journal-article","created":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T11:51:54Z","timestamp":1536925914000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Inner\u2013outer factorization for differential-algebraic systems"],"prefix":"10.1007","volume":"30","author":[{"given":"Timo","family":"Reis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Voigt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,9,14]]},"reference":[{"key":"221_CR1","series-title":"Differential-algebraic equations forum","first-page":"1","volume-title":"Surveys in differential-algebraic equations\u00a0I","author":"T Berger","year":"2013","unstructured":"Berger T, Reis T (2013) Controllability of linear differential-algebraic systems\u2014a survey. In: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations\u00a0I. Differential-algebraic equations forum. Springer, Berlin, pp 1\u201361"},{"key":"221_CR2","series-title":"Differential-algebraic equations forum","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/978-3-319-46618-7_4","volume-title":"Surveys in differential-algebraic equations\u00a0IV","author":"T Berger","year":"2017","unstructured":"Berger T, Reis T, Trenn S (2017) Observability of linear differential-algebraic systems: a survey. In: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations\u00a0IV. Differential-algebraic equations forum. Springer, Cham, pp 161\u2013219"},{"issue":"1","key":"221_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/0610001","volume":"10","author":"T Chen","year":"1989","unstructured":"Chen T, Francis BA (1989) Spectral and inner\u2013outer factorizations of rational matrices. SIAM J Matrix Anal Appl 10(1):1\u201317","journal-title":"SIAM J Matrix Anal Appl"},{"key":"221_CR4","series-title":"Lecture notes in control and information science","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0007371","volume-title":"A course in $$H_\\infty $$ H \u221e","author":"BA Francis","year":"1987","unstructured":"Francis BA (1987) A course in \n                    \n                      \n                    \n                    $$H_\\infty $$\n                    \n                      \n                        \n                          H\n                          \u221e\n                        \n                      \n                    \n                   control theory, vol 88. Lecture notes in control and information science. Springer, Heidelberg"},{"issue":"2","key":"221_CR5","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/0167-6911(88)90081-3","volume":"11","author":"M Green","year":"1988","unstructured":"Green M (1988) On inner\u2013outer factorization. Syst Control Lett 11(2):93\u201397","journal-title":"Syst Control Lett"},{"issue":"11","key":"221_CR6","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1109\/TAC.2002.804466","volume":"47","author":"G Gu","year":"2002","unstructured":"Gu G (2002) Inner\u2013outer factorization for strictly proper transfer matrices. IEEE Trans Autom Control 47(11):1915\u20131919","journal-title":"IEEE Trans Autom Control"},{"issue":"3","key":"221_CR7","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0167-6911(91)90046-H","volume":"16","author":"S Hara","year":"1991","unstructured":"Hara S, Sugie T (1991) Inner\u2013outer factorization for strictly proper functions with \n                    \n                      \n                    \n                    $$j\\omega $$\n                    \n                      \n                        \n                          j\n                          \u03c9\n                        \n                      \n                    \n                  -axis zeros. Syst Control Lett 16(3):179\u2013185","journal-title":"Syst Control Lett"},{"issue":"2","key":"221_CR8","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1051\/cocv\/2015051","volume":"23","author":"A Ilchmann","year":"2017","unstructured":"Ilchmann A, Reis T (2017) Outer transfer functions of differential-algebraic systems. ESAIM Control Optim Calc Var 23(2):391\u2013425","journal-title":"ESAIM Control Optim Calc Var"},{"issue":"12","key":"221_CR9","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1515\/auto.2013.1002","volume":"61","author":"A Ilchmann","year":"2013","unstructured":"Ilchmann A, Wirth F (2013) On minimum phase. at-Automatisierungstechnik 61(12):805\u2013817","journal-title":"at-Automatisierungstechnik"},{"key":"221_CR10","volume-title":"Linear systems","author":"T Kailath","year":"1980","unstructured":"Kailath T (1980) Linear systems. Prentice Hall, Englewood Cliffs"},{"issue":"1","key":"221_CR11","first-page":"269","volume":"49","author":"H Kimura","year":"1989","unstructured":"Kimura H (1989) Conjugation, interpolation, and model matching in \n                    \n                      \n                    \n                    $$H^{\\infty }$$\n                    \n                      \n                        \n                          H\n                          \u221e\n                        \n                      \n                    \n                  . Intern J Control 49(1):269\u2013307","journal-title":"Intern J Control"},{"key":"221_CR12","series-title":"Graduate texts in mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1871-3","volume-title":"Complex analysis","author":"S Lang","year":"1985","unstructured":"Lang S (1985) Complex analysis, vol 103, 2nd edn. Graduate texts in mathematics. Springer, New York","edition":"2"},{"issue":"12","key":"221_CR13","doi-asserted-by":"publisher","first-page":"2307","DOI":"10.1109\/9.895566","volume":"45","author":"C Oar\u0103","year":"2000","unstructured":"Oar\u0103 C, Varga A (2000) Computation of general inner\u2013outer and spectral factorizations. IEEE Trans Autom Control 45(12):2307\u20132325","journal-title":"IEEE Trans Autom Control"},{"key":"221_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2953-5","volume-title":"Introduction to mathematical systems theory. A behavioral approach","author":"JW Polderman","year":"1998","unstructured":"Polderman JW, Willems JC (1998) Introduction to mathematical systems theory. A behavioral approach. Springer, New York"},{"key":"221_CR15","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1016\/j.laa.2010.09.005","volume":"434","author":"T Reis","year":"2011","unstructured":"Reis T (2011) Lur\u2019e equations and even matrix pencils. Linear Algebra Appl 434:152\u2013173","journal-title":"Linear Algebra Appl"},{"key":"221_CR16","series-title":"Modeling and simulation in science, engineering and technology","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/978-3-319-08437-4_2","volume-title":"Large-scale networks in engineering and life sciences","author":"T Reis","year":"2014","unstructured":"Reis T (2014) Mathematical modeling and analysis of nonlinear time-invariant RLC circuits. In: Benner P, Findeisen R, Flockerzi D, Reichl U, Sundmacher K (eds) Large-scale networks in engineering and life sciences, 2nd edn. Modeling and simulation in science, engineering and technology. Birk\u00e4user, Basel, pp 125\u2013198","edition":"2"},{"issue":"1","key":"221_CR17","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1002\/pamm.201410395","volume":"14","author":"T Reis","year":"2014","unstructured":"Reis T, Rendel O (2014) Numerical solution of singular Lur\u2019e equations. Proc Appl Math Mech 14(1):829\u2013830","journal-title":"Proc Appl Math Mech"},{"key":"221_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.sysconle.2015.09.003","volume":"86","author":"T Reis","year":"2015","unstructured":"Reis T, Voigt M (2015) The Kalman\u2013Yakubovich\u2013Popov inequality for differential-algebraic systems: existence of nonpositive solutions. Syst Control Lett 86:1\u20138","journal-title":"Syst Control Lett"},{"key":"221_CR19","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.laa.2015.06.021","volume":"485","author":"T Reis","year":"2015","unstructured":"Reis T, Rendel O, Voigt M (2015) The Kalman\u2013Yakubovich\u2013Popov inequality for differential-algebraic systems. Linear Algebra Appl 485:153\u2013193","journal-title":"Linear Algebra Appl"},{"key":"221_CR20","unstructured":"Reis T, Rendel O (2016) Numerical solution of matrix equations arising in linear-quadratic optimal control of differential-algebraic equations. Hamburger Beitr\u00e4ge zur Angewandten Mathematik 2016-36, Universit\u00e4t Hamburg, Fachbereich Mathematik. \n                    https:\/\/preprint.math.uni-hamburg.de\/public\/papers\/hbam\/hbam2016-36.pdf"},{"issue":"4","key":"221_CR21","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.1080\/00207178708933797","volume":"45","author":"S Tan","year":"1987","unstructured":"Tan S, Vandewalle J (1987) Realization algorithm for determining generalized state-space representations. Intern J Control 45(4):1137\u20131146","journal-title":"Intern J Control"},{"issue":"3","key":"221_CR22","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/0167-6911(93)90062-B","volume":"20","author":"MC Tsai","year":"1993","unstructured":"Tsai MC, Chen LW (1993) A numerical algorithm for inner\u2013outer factorizations for real-rational matrices. Syst Control Lett 20(3):209\u2013217","journal-title":"Syst Control Lett"},{"key":"221_CR23","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/0024-3795(90)90144-2","volume":"137\u2013138","author":"P Dooren Van","year":"1990","unstructured":"Van Dooren P (1990) Rational and polynomial matrix factorizations via recursive pole-zero cancellation. Linear Algebra Appl 137\u2013138:663\u2013697","journal-title":"Linear Algebra Appl"},{"issue":"5","key":"221_CR24","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1109\/9.668836","volume":"43","author":"A Varga","year":"1998","unstructured":"Varga A (1998) Computation of inner\u2013outer factorizations of rational matrices. IEEE Trans Autom Control 43(5):684\u2013688","journal-title":"IEEE Trans Autom Control"},{"key":"221_CR25","unstructured":"Voigt M (2015) On linear-quadratic optimal control and robustness of differential-algebraic systems. Logos-Verlag, Berlin. Also as Dissertation. Otto-von-Guericke-Universit\u00e4t Magdeburg, Fakult\u00e4t f\u00fcr Mathematik"},{"issue":"3","key":"221_CR26","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1109\/9.280787","volume":"39","author":"M Weiss","year":"1994","unstructured":"Weiss M (1994) Spectral and inner\u2013outer factorizations through the constrained Riccati equation. IEEE Trans Autom Control 39(3):677\u2013681","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"221_CR27","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1080\/002071798221975","volume":"71","author":"X Xin","year":"1998","unstructured":"Xin X, Mita T (1998) Inner\u2013outer factorization for non-square proper functions with infinite and finite \n                    \n                      \n                    \n                    $$j\\omega $$\n                    \n                      \n                        \n                          j\n                          \u03c9\n                        \n                      \n                    \n                  -axis zeros. Intern J Control 71(1):145\u2013161","journal-title":"Intern J Control"},{"issue":"1","key":"221_CR28","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/0167-6911(90)90077-8","volume":"14","author":"F-B Yeh","year":"1990","unstructured":"Yeh F-B, Wei L-F (1990) Inner\u2013outer factorizations of right-invertible real-rational matrices. Syst Control Lett 14(1):31\u201336","journal-title":"Syst Control Lett"},{"key":"221_CR29","volume-title":"Robust and optimal control","author":"K Zhou","year":"1996","unstructured":"Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice-Hall, Englewood Cliffs"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00498-018-0221-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-018-0221-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-018-0221-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T20:53:12Z","timestamp":1569358392000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00498-018-0221-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["221"],"URL":"https:\/\/doi.org\/10.1007\/s00498-018-0221-5","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]},"assertion":[{"value":"25 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 August 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"15"}}