{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:39:55Z","timestamp":1771677595441,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T00:00:00Z","timestamp":1653955200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T00:00:00Z","timestamp":1653955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["314838170"],"award-info":[{"award-number":["314838170"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["314838170"],"award-info":[{"award-number":["314838170"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["314838170"],"award-info":[{"award-number":["314838170"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s11075-022-01331-w","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T16:29:56Z","timestamp":1654014596000},"page":"1083-1103","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A low-rank solution method for Riccati equations with indefinite quadratic terms"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3362-4103","authenticated-orcid":false,"given":"Peter","family":"Benner","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0228-8522","authenticated-orcid":false,"given":"Jan","family":"Heiland","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1667-4862","authenticated-orcid":false,"given":"Steffen W. R.","family":"Werner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"key":"1331_CR1","volume-title":"Network Analysis and Synthesis: A Modern Systems Approach. Networks Series","author":"BDO Anderson","year":"1972","unstructured":"Anderson, B.D.O., Vongpanitlerd, B.: Network Analysis and Synthesis: A Modern Systems Approach. Networks Series. Prentice-Hall, Englewood Cliffs (1972)"},{"issue":"12","key":"1331_CR2","doi-asserted-by":"publisher","first-page":"1746","DOI":"10.1109\/PROC.1984.13083","volume":"72","author":"WF Arnold","year":"1984","unstructured":"Arnold, W.F., Laub, A.J.: Generalized eigenproblem algorithms and software for algebraic Riccati equations. Proc. IEEE 72(12), 1746\u20131754 (1984). https:\/\/doi.org\/10.1109\/PROC.1984.13083","journal-title":"Proc. IEEE"},{"issue":"2","key":"1331_CR3","doi-asserted-by":"publisher","first-page":"A832","DOI":"10.1137\/140980016","volume":"37","author":"E B\u00e4nsch","year":"2015","unstructured":"B\u00e4nsch, E., Benner, P., Saak, J., Weichelt, H.K.: Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows. SIAM J. Sci. Comput. 37(2), A832\u2013A858 (2015). https:\/\/doi.org\/10.1137\/140980016","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"1331_CR4","doi-asserted-by":"publisher","first-page":"9547","DOI":"10.1016\/j.ifacol.2017.08.1625","volume":"50","author":"T Ba\u015far","year":"2017","unstructured":"Ba\u015far, T., Moon, J.: Riccati equations in Nash and Stackelberg differential and dynamic games. IFAC-Pap. 50(1), 9547\u20139554 (2017). https:\/\/doi.org\/10.1016\/j.ifacol.2017.08.1625, 20th IFAC World Congress","journal-title":"IFAC-Pap."},{"key":"1331_CR5","doi-asserted-by":"publisher","unstructured":"Benner, P.: Partial Stabilization of Descriptor Systems Using Spectral Projectors. In: Van Dooren, P., Bhattacharyya, S.P., Chan, R. H., Olshevsky, V., Routray, A. (eds.) Numerical Linear Algebra in Signals, Systems and Control, Lect. Notes Electr. Eng. https:\/\/doi.org\/10.1007\/978-94-007-0602-6_3, vol. 80, pp 55\u201376. Springer, Dodrecht (2011)","DOI":"10.1007\/978-94-007-0602-6_3"},{"key":"1331_CR6","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/j.laa.2015.09.027","volume":"488","author":"P Benner","year":"2016","unstructured":"Benner, P., Bujanovi\u0107, Z.: On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces. Linear Algebra Appl. 488, 430\u2013459 (2016). https:\/\/doi.org\/10.1016\/j.laa.2015.09.027https:\/\/doi.org\/10.1016\/j.laa.2015.09.027","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"1331_CR7","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00211-017-0907-5","volume":"138","author":"P Benner","year":"2018","unstructured":"Benner, P., Bujanovi\u0107, Z., K\u00fcrschner, P., Saak, J.: RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations. Numer. Math. 138(2), 301\u2013330 (2018). https:\/\/doi.org\/10.1007\/s00211-017-0907-5https:\/\/doi.org\/10.1007\/s00211-017-0907-5","journal-title":"Numer. Math."},{"issue":"2","key":"1331_CR8","doi-asserted-by":"publisher","first-page":"A957","DOI":"10.1137\/18M1220960","volume":"42","author":"P Benner","year":"2020","unstructured":"Benner, P., Bujanovi\u0107, Z., K\u00fcrschner, P., Saak, J.: A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems. SIAM J. Sci. Comput. 42(2), A957\u2013A996 (2020). https:\/\/doi.org\/10.1137\/18M1220960","journal-title":"SIAM J. Sci. Comput."},{"key":"1331_CR9","doi-asserted-by":"publisher","unstructured":"Benner, P., Ezzatti, P., Quintana-ort\u00ed, E.S., Rem\u00f3, n, A.: A factored variant of the Newton iteration for the solution of algebrai Riccati equations via the matrix sign function. Numer. Algorithms 66(2), 363\u2013377 (2014). https:\/\/doi.org\/10.1007\/s11075-013-9739-2","DOI":"10.1007\/s11075-013-9739-2"},{"key":"1331_CR10","doi-asserted-by":"publisher","unstructured":"Benner, P., Heiland, J.: Equivalence of Riccati-based robust controller design for index-1 descriptor systems and standard plants with feedthrough. In: 2020 European Control Conference (ECC), pp. 402\u2013407, https:\/\/doi.org\/10.23919\/ECC51009.2020.9143771 (2020)","DOI":"10.23919\/ECC51009.2020.9143771"},{"key":"1331_CR11","doi-asserted-by":"publisher","unstructured":"Benner, P., Heiland, J., Werner, S.W.R.: Robust output-feedback stabilization for incompressible flows using low-dimensional ${\\mathscr{H}}_{\\infty }$-controllers. Comput. Optim. Appl., https:\/\/doi.org\/10.1007\/s10589-022-00359-xhttps:\/\/doi.org\/10.1007\/s10589-022-00359-x (2022)","DOI":"10.1007\/s10589-022-00359-x 10.1007\/s10589-022-00359-x"},{"issue":"9","key":"1331_CR12","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1002\/nla.622","volume":"15","author":"P Benner","year":"2008","unstructured":"Benner, P., Li, J.R., Penzl, T.: Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. Numer. Lin. Alg. Appl. 15(9), 755\u2013777 (2008). https:\/\/doi.org\/10.1002\/nla.622","journal-title":"Numer. Lin. Alg. Appl."},{"issue":"1","key":"1331_CR13","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1002\/gamm.201310003","volume":"36","author":"P Benner","year":"2013","unstructured":"Benner, P., Saak, J.: Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: A state of the art survey. GAMM-Mitt. 36(1), 32\u201352 (2013). https:\/\/doi.org\/10.1002\/gamm.201310003","journal-title":"GAMM-Mitt."},{"issue":"2","key":"1331_CR14","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1137\/130923993","volume":"52","author":"P Benner","year":"2014","unstructured":"Benner, P., Stykel, T.: Numerical solution of projected algebraic Riccati equations. SIAM J. Numer. Anal. 52(2), 581\u2013600 (2014). https:\/\/doi.org\/10.1137\/130923993","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1331_CR15","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1016\/j.ifacol.2018.03.092","volume":"51","author":"P Benner","year":"2018","unstructured":"Benner, P., Werner, S.W.R.: Model reduction of descriptor systems with the MORLAB toolbox. IFAC-Pap 51 (2), 547\u2013552 (2018). https:\/\/doi.org\/10.1016\/j.ifacol.2018.03.092, 9th Vienna International Conference on Mathematical Modelling MATHMOD 2018","journal-title":"IFAC-Pap"},{"key":"1331_CR16","doi-asserted-by":"publisher","unstructured":"Benner, P., Werner, S.W.R.: MORLAB \u2013 Model Order Reduction LABoratory (version 5.0). https:\/\/doi.org\/10.5281\/zenodo.3332716. https:\/\/www.mpi-magdeburg.mpg.de\/projects\/morlab (2019)","DOI":"10.5281\/zenodo.3332716"},{"issue":"2","key":"1331_CR17","doi-asserted-by":"publisher","first-page":"750","DOI":"10.1137\/050639089","volume":"46","author":"MC Delfour","year":"2007","unstructured":"Delfour, M.C.: Linear quadratic differential games: saddle point and Riccati differential equation. SIAM J. Control Optim. 46(2), 750\u2013774 (2007). https:\/\/doi.org\/10.1137\/050639089","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"1331_CR18","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1109\/TPWRS.2008.926693","volume":"23","author":"F Freitas","year":"2008","unstructured":"Freitas, F., Rommes, J., Martins, N.: Gramian-based reduction method applied to large sparse power system descriptor models. IEEE Trans. Power Syst. 23(3), 1258\u20131270 (2008). https:\/\/doi.org\/10.1109\/TPWRS.2008.926693https:\/\/doi.org\/10.1109\/TPWRS.2008.926693","journal-title":"IEEE Trans. Power Syst."},{"key":"1331_CR19","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 4th edn. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore (2013)","edition":"4th edn."},{"key":"1331_CR20","doi-asserted-by":"publisher","unstructured":"Heiland, J., Werner, S.W.R.: Code, data and results for numerical experiments in \u201cRobust output-feedback stabilization for incompressible flows using low-dimensional ${\\mathscr{H}}_{\\infty }$-controllers\u201d (version 2.0). https:\/\/doi.org\/10.5281\/zenodo.5532539 (2021)","DOI":"10.5281\/zenodo.5532539"},{"issue":"2","key":"1331_CR21","doi-asserted-by":"publisher","first-page":"1038","DOI":"10.1137\/070681910","volume":"30","author":"M Heinkenschloss","year":"2008","unstructured":"Heinkenschloss, M., Sorensen, D.C., Sun, K.: Balanced truncation model reduction for a class of descriptor systems with application to the Oseen equations. SIAM J. Sci. Comput. 30(2), 1038\u20131063 (2008). https:\/\/doi.org\/10.1137\/070681910","journal-title":"SIAM J. Sci. Comput."},{"key":"1331_CR22","first-page":"53","volume":"33","author":"M Heyouni","year":"2009","unstructured":"Heyouni, M., Jbilou, K.: An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation. Electron. Trans. Numer. Anal. 33, 53\u201362 (2009). {https:\/\/etna.math.kent.edu\/volumes\/2001-2010\/vol33\/abstract.php}","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"10","key":"1331_CR23","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1109\/TAC.1983.1103159","volume":"28","author":"EA Jonckheere","year":"1983","unstructured":"Jonckheere, E.A., Silverman, L.M.: A new set of invariants for linear systems\u2013application to reduced order compensator design. IEEE Trans. Autom. Control 28(10), 953\u2013964 (1983). https:\/\/doi.org\/10.1109\/TAC.1983.1103159","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"1331_CR24","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1109\/TAC.1968.1098829","volume":"13","author":"DL Kleinman","year":"1968","unstructured":"Kleinman, D.L.: On an iterative technique for Riccati equation computations. IEEE Trans. Autom. Control 13(1), 114\u2013115 (1968). https:\/\/doi.org\/10.1109\/TAC.1968.1098829","journal-title":"IEEE Trans. Autom. Control"},{"key":"1331_CR25","unstructured":"K\u00fcrschner, P.: Efficient low-rank solution of large-scale matrix equations. Dissertation, Otto-von-Guericke-Universit\u00e4t, Magdeburg, Germany, http:\/\/hdl.handle.net\/11858\/00-001M-0000-0029-CE18-2http:\/\/hdl.handle.net\/11858\/00-001M-0000-0029-CE18-2 (2016)"},{"key":"1331_CR26","doi-asserted-by":"publisher","unstructured":"Lanzon, A., Feng, Y., Anderson, B.D.O.: An Iterative Algorithm to Solve Algebraic Riccati Equations with an Indefinite Quadratic Term. In: 2007 European Control Conference (ECC), pp. 3033\u20133039. https:\/\/doi.org\/10.23919\/ecc.2007.7068239(2007)","DOI":"10.23919\/ecc.2007.7068239"},{"issue":"10","key":"1331_CR27","doi-asserted-by":"publisher","first-page":"2280","DOI":"10.1109\/TAC.2008.2006108","volume":"53","author":"A Lanzon","year":"2008","unstructured":"Lanzon, A., Feng, Y., Anderson, B.D.O., Rotkowitz, M.: Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method. IEEE Trans. Autom. Control 53(10), 2280\u20132291 (2008). https:\/\/doi.org\/10.1109\/TAC.2008.2006108","journal-title":"IEEE Trans. Autom. Control"},{"issue":"6","key":"1331_CR28","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1109\/TAC.1979.1102178","volume":"24","author":"AJ Laub","year":"1979","unstructured":"Laub, A.J.: A Schur method for solving algebraic Riccati equations. IEEE Trans. Autom. Control 24(6), 913\u2013921 (1979). https:\/\/doi.org\/10.1109\/TAC.1979.1102178","journal-title":"IEEE Trans. Autom. Control"},{"key":"1331_CR29","unstructured":"Leibfritz, F.: COMPleib: Constrained matrix-optimization Problem library \u2013 a collection of test examples for nonlinear semidefinite programs, control system design and related problems. Tech.-report, University of Trier. http:\/\/www.friedemann-leibfritz.de\/COMPlib_Data\/COMPlib_Main_Paper.pdf (2004)"},{"issue":"1","key":"1331_CR30","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1137\/S0895479801384937","volume":"24","author":"JR Li","year":"2002","unstructured":"Li, J.R., White, J.: Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl. 24(1), 260\u2013280 (2002). https:\/\/doi.org\/10.1137\/S0895479801384937","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"1331_CR31","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1002\/nla.1936","volume":"22","author":"Y Lin","year":"2015","unstructured":"Lin, Y., Simoncini, V.: A new subspace iteration method for the algebraic Riccati equation. Numer. Linear Algebra Appl. 22(1), 26\u201347 (2015). https:\/\/doi.org\/10.1002\/nla.1936","journal-title":"Numer. Linear Algebra Appl."},{"key":"1331_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8328-3","volume-title":"Optimal Control: An Introduction","author":"A Locatelli","year":"2001","unstructured":"Locatelli, A.: Optimal Control: An Introduction. Birkh\u00e4user, Basel (2001)"},{"key":"1331_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/BFB0043199 10.1007\/BFB0043199","volume-title":"Robust Controller Design Using Normalized Coprime Factor Plant Descriptions, Lect. Notes Control Inf. Sci., vol. 138","author":"DC McFarlane","year":"1990","unstructured":"McFarlane, D.C., Glover, K.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions, Lect. Notes Control Inf. Sci., vol. 138. Springer, Berlin (1990). https:\/\/doi.org\/10.1007\/BFB0043199https:\/\/doi.org\/10.1007\/BFB0043199"},{"issue":"10","key":"1331_CR34","doi-asserted-by":"publisher","first-page":"1627","DOI":"10.1080\/00207179.2011.622791","volume":"84","author":"J M\u00f6ckel","year":"2011","unstructured":"M\u00f6ckel, J., Reis, T., Stykel, T.: Linear-quadratic Gaussian balancing for model reduction of differential-algebraic systems. Internat. J. Control 84(10), 1627\u20131643 (2011). https:\/\/doi.org\/10.1080\/00207179.2011.622791https:\/\/doi.org\/10.1080\/00207179.2011.622791","journal-title":"Internat. J. Control"},{"issue":"2","key":"1331_CR35","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1109\/31.1720","volume":"35","author":"PC Opdenacker","year":"1988","unstructured":"Opdenacker, P.C., Jonckheere, E.A.: A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds. IEEE Trans. Circuits Syst. 35(2), 184\u2013189 (1988). https:\/\/doi.org\/10.1109\/31.1720","journal-title":"IEEE Trans. Circuits Syst."},{"issue":"4","key":"1331_CR36","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1080\/00207178008922881","volume":"32","author":"JD Roberts","year":"1980","unstructured":"Roberts, J.D.: Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Internat. J. Control 32(4), 677\u2013687 (1980). https:\/\/doi.org\/10.1080\/00207178008922881, Reprint of Technical Report No. TR-13, CUED\/B-Control, Cambridge University, Engineering Department, 1971","journal-title":"Internat. J. Control"},{"key":"1331_CR37","unstructured":"Saak, J.: Efficient numerical solution of large scale algebraic matrix equations in PDE control and model order reduction. Dissertation, Technische Universit\u00e4t Chemnitz, Germany. https:\/\/nbn-resolving.org\/urn:nbn:de:bsz:ch1-200901642 (2009)"},{"key":"1331_CR38","doi-asserted-by":"publisher","unstructured":"Saak, J, K\u00f6hler, M, Benner, P: M-M.E.S.S. \u2013 The matrix equations sparse solvers library (version 2.1). https:\/\/doi.org\/10.5281\/zenodo.4719688, https:\/\/www.mpi-magdeburg.mpg.de\/projects\/mess (2021)","DOI":"10.5281\/zenodo.4719688"},{"issue":"2","key":"1331_CR39","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1016\/j.ifacol.2018.03.112","volume":"51","author":"J Saak","year":"2018","unstructured":"Saak, J., Voigt, M.: Model reduction of constrained mechanical systems in M-M.E.S.S. IFAC-Pap 51(2), 661\u2013666 (2018). https:\/\/doi.org\/10.1016\/j.ifacol.2018.03.112, 9th Vienna International Conference on Mathematical Modelling MATHMOD 2018","journal-title":"IFAC-Pap"},{"issue":"3","key":"1331_CR40","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1109\/TAC.1974.1100536","volume":"19","author":"N Sandell","year":"1974","unstructured":"Sandell, N.: On Newton\u2019s method for Riccati equation solution. IEEE Trans. Autom. Control 19(3), 254\u2013255 (1974). https:\/\/doi.org\/10.1109\/TAC.1974.1100536","journal-title":"IEEE Trans. Autom. Control"},{"issue":"4","key":"1331_CR41","doi-asserted-by":"publisher","first-page":"1655","DOI":"10.1137\/16M1059382","volume":"37","author":"V Simoncini","year":"2016","unstructured":"Simoncini, V.: Analysis of the rational Krylov subspace projection method for large-scale algebraic Riccati equations. SIAM J. Matrix Anal. Appl. 37 (4), 1655\u20131674 (2016). https:\/\/doi.org\/10.1137\/16M1059382","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"5","key":"1331_CR42","doi-asserted-by":"publisher","first-page":"3598","DOI":"10.1137\/18M1178815","volume":"56","author":"T Stillfjord","year":"2018","unstructured":"Stillfjord, T.: Singular value decay of operator-valued differential Lyapunov and Riccati equations. SIAM J. Control Optim. 56(5), 3598\u20133618 (2018). https:\/\/doi.org\/10.1137\/18M1178815","journal-title":"SIAM J. Control Optim."},{"key":"1331_CR43","first-page":"187","volume":"30","author":"T Stykel","year":"2008","unstructured":"Stykel, T.: Low-rank iterative methods for projected generalized Lyapunov equations. Electron. Trans. Numer. Anal. 30, 187\u2013202 (2008). https:\/\/etna.math.kent.edu\/volumes\/2001-2010\/vol30\/abstract.php","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"4","key":"1331_CR44","first-page":"2005","volume":"10","author":"A Varga","year":"1995","unstructured":"Varga, A.: On computing high accuracy solutions of a class of Riccati equations. Control-Theory and Adv. Technol. 10(4), 2005\u20132016 (1995)","journal-title":"Control-Theory and Adv. Technol."},{"key":"1331_CR45","doi-asserted-by":"publisher","unstructured":"Weichelt, H.K.: Numerical aspects of flow stabilization by Riccati feedback. Dissertation, Otto-Von-Guericke-Universit\u00e4t, Magdeburg, Germany. https:\/\/doi.org\/10.25673\/4493 (2016)","DOI":"10.25673\/4493"},{"issue":"112","key":"1331_CR46","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1007\/s12190-019-01303-9","volume":"371","author":"L Zhang","year":"2020","unstructured":"Zhang, L., Fan, H.Y., Chu, E.K.: Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations. J. Comput. Appl. Math. 371(112), 685 (2020). https:\/\/doi.org\/10.1016\/j.cam.2019.112685","journal-title":"J. Comput. Appl. Math."},{"key":"1331_CR47","volume-title":"Robust and Optimal Control","author":"K Zhou","year":"1996","unstructured":"Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice-Hall, Upper Saddle (1996)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01331-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-022-01331-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01331-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T08:32:15Z","timestamp":1673512335000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-022-01331-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,31]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["1331"],"URL":"https:\/\/doi.org\/10.1007\/s11075-022-01331-w","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,31]]},"assertion":[{"value":"16 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Parts of this work were carried out while Werner was at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Germany. Benner is a member of the editorial board of Numerical Algorithms. The authors declare to have no competing interests related to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Competing interests"}}]}}