{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T14:21:04Z","timestamp":1768314064130,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,11,11]],"date-time":"2017-11-11T00:00:00Z","timestamp":1510358400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Institut Farman","award":["project SWITCHDESIGN"],"award-info":[{"award-number":["project SWITCHDESIGN"]}]},{"name":"Agence Nationale de la Recherche (FR)","award":["ANR-11-IDEX-0003-02"],"award-info":[{"award-number":["ANR-11-IDEX-0003-02"]}]},{"name":"Agence Nationale de la Recherche (FR)","award":["NR-11-LABEX- 0045-DIGICOSME"],"award-info":[{"award-number":["NR-11-LABEX- 0045-DIGICOSME"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Form Methods Syst Des"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s10703-017-0305-8","type":"journal-article","created":{"date-parts":[[2017,11,11]],"date-time":"2017-11-11T08:15:01Z","timestamp":1510388101000},"page":"363-383","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An improved algorithm for the control synthesis of nonlinear sampled switched systems"],"prefix":"10.1007","volume":"53","author":[{"given":"Adrien","family":"Le Co\u00ebnt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julien","family":"Alexandre dit Sandretto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7230-0710","authenticated-orcid":false,"given":"Alexandre","family":"Chapoutot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Fribourg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,11,11]]},"reference":[{"key":"305_CR1","doi-asserted-by":"crossref","unstructured":"Alur R, Courcoubetis C, Henzinger TA, Ho P-H (1993) Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Proceedings of hybrid systems I, number 736 in LNCS, Springer, pp 209\u2013229","DOI":"10.1007\/3-540-57318-6_30"},{"issue":"3","key":"305_CR2","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s10703-014-0211-2","volume":"45","author":"L Fribourg","year":"2014","unstructured":"Fribourg L, K\u00fchne U, Soulat R (2014) Finite controlled invariants for sampled switched systems. Form Methods Syst Des 45(3):303\u2013329","journal-title":"Form Methods Syst Des"},{"key":"305_CR3","volume-title":"Switching in systems and control","author":"D Liberzon","year":"2012","unstructured":"Liberzon D (2012) Switching in systems and control. Springer, London"},{"key":"305_CR4","doi-asserted-by":"crossref","unstructured":"Girard A (2005) Reachability of uncertain linear systems using zonotopes. In: Proceedings of hybrid systems: computation and control, volume 3414 of LNCS, Springer, pp 291\u2013305","DOI":"10.1007\/978-3-540-31954-2_19"},{"key":"305_CR5","doi-asserted-by":"crossref","unstructured":"Althoff M (2013) Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets. In: ACM proceedings of hybrid systems: computation and control, pp 173\u2013182","DOI":"10.1145\/2461328.2461358"},{"key":"305_CR6","doi-asserted-by":"crossref","unstructured":"Chen X, \u00c1brah\u00e1m E, Sankaranarayanan S (2013) Flow*: an analyzer for non-linear hybrid systems. In: Proceedings of computer aided verification, volume 8044 of LNCS, Springer, pp 258\u2013263","DOI":"10.1007\/978-3-642-39799-8_18"},{"key":"305_CR7","doi-asserted-by":"crossref","unstructured":"Frehse G, Guernic CL, Donz\u00e9 A, Cotton S, Ray R, Lebeltel O, Ripado R, Girard A, Dang T, Maler O (2011) SpaceEx: scalable verification of hybrid systems. In: Proceedings of computer aided verification, volume 6806 of LNCS, Springer, pp 379\u2013395","DOI":"10.1007\/978-3-642-22110-1_30"},{"key":"305_CR8","volume-title":"Interval analysis","author":"R Moore","year":"1966","unstructured":"Moore R (1966) Interval analysis. Prentice Hall, Englewood Cliffs"},{"issue":"1","key":"305_CR9","first-page":"21","volume":"105","author":"NS Nedialkov","year":"1999","unstructured":"Nedialkov NS, R KJ, Corliss GF (1999) Validated solutions of initial value problems for ordinary differential equations. Appl Math Comput 105(1):21\u201368","journal-title":"Appl Math Comput"},{"issue":"10","key":"305_CR10","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1016\/j.apnum.2006.10.006","volume":"57","author":"Y Lin","year":"2007","unstructured":"Lin Y, Stadtherr MA (2007) Validated solutions of initial value problems for parametric ODEs. Appl Numer Math 57(10):1145\u20131162","journal-title":"Appl Numer Math"},{"issue":"1","key":"305_CR11","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s11075-014-9889-x","volume":"69","author":"T Dzetkuli\u010d","year":"2015","unstructured":"Dzetkuli\u010d T (2015) Rigorous integration of non-linear ordinary differential equations in Chebyshev basis. Numer Algorithms 69(1):183\u2013205","journal-title":"Numer Algorithms"},{"key":"305_CR12","doi-asserted-by":"crossref","unstructured":"Bouissou O, Martel M (2006) GRKLib: a guaranteed Runge Kutta library. In: IEEE Proceedings of scientific computing, computer arithmetic and validated numerics","DOI":"10.1109\/SCAN.2006.20"},{"key":"305_CR13","doi-asserted-by":"crossref","unstructured":"Gajda K, Jankowska M, Marciniak A, Szyszka B (2008) A survey of interval Runge\u2013Kutta and multistep methods for solving the initial value problem. In: Proceedings of parallel processing and applied mathematics, volume 4967 of LNCS, Springer, pp 1361\u20131371","DOI":"10.1007\/978-3-540-68111-3_144"},{"key":"305_CR14","doi-asserted-by":"crossref","unstructured":"Bouissou O, Chapoutot A, Djoudi A (2013) Enclosing temporal evolution of dynamical systems using numerical methods. In: Proceedings of NASA formal methods, number 7871 in LNCS, Springer, pp 108\u2013123","DOI":"10.1007\/978-3-642-38088-4_8"},{"key":"305_CR15","unstructured":"Alexandre dit Sandretto J, Chapoutot A (2016) Validated explicit and implicit Runge\u2013Kutta methods. Reliab Comput 22"},{"key":"305_CR16","doi-asserted-by":"crossref","unstructured":"Henzinger TA, Horowitz B, Majumdar R, Wong-Toi H (2000) Beyond HYTECH: hybrid systems analysis using interval numerical methods. In: Proceedings of hybrid systems: computational and control, volume 1790 of LNCS, Springer, pp 130\u2013144","DOI":"10.1007\/3-540-46430-1_14"},{"issue":"1","key":"305_CR17","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TAC.2009.2034922","volume":"55","author":"A Girard","year":"2010","unstructured":"Girard A, Pola G, Tabuada P (2010) Approximately bisimilar symbolic models for incrementally stable switched systems. IEEE Trans Autom Control 55(1):116\u2013126","journal-title":"IEEE Trans Autom Control"},{"issue":"7","key":"305_CR18","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1109\/TAC.2011.2176409","volume":"57","author":"M Zamani","year":"2012","unstructured":"Zamani M, Pola G, Mazo M, Tabuada P (2012) Symbolic models for nonlinear control systems without stability assumptions. IEEE Trans Autom Control 57(7):1804\u20131809","journal-title":"IEEE Trans Autom Control"},{"issue":"4","key":"305_CR19","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1109\/TAC.2016.2593947","volume":"62","author":"G Reissig","year":"2017","unstructured":"Reissig G, Weber A, Rungger M (2017) Feedback refinement relations for the synthesis of symbolic controllers. IEEE Trans Autom Control 62(4):1781\u20131796","journal-title":"IEEE Trans Autom Control"},{"key":"305_CR20","doi-asserted-by":"crossref","unstructured":"Le Co\u00ebnt A, Alexandre dit Sandretto J, Chapoutot A, Fribourg L (2016) Control of nonlinear switched systems based on validated simulation. In: IEEE Proceedings of symbolic and numerical methods for reachability analysis, pp 1\u20136","DOI":"10.1109\/SNR.2016.7479377"},{"key":"305_CR21","doi-asserted-by":"crossref","unstructured":"Ravanbakhsh H, Sankaranarayanan S (2016) Robust controller synthesis of switched systems using counterexample guided framework. In: ACM\/IEEE proceedings of conference on embedded software, pp 1\u201310","DOI":"10.1145\/2968478.2968485"},{"key":"305_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-0249-6","volume-title":"Applied interval analysis","author":"L Jaulin","year":"2001","unstructured":"Jaulin L, Kieffer M, Didrit O, Walter E (2001) Applied interval analysis. Springer, London"},{"key":"305_CR23","volume-title":"Solving ordinary differential equations\u00a0I: nonstiff problems","author":"E Hairer","year":"2009","unstructured":"Hairer E, Norsett SP, Wanner G (2009) Solving ordinary differential equations\u00a0I: nonstiff problems, 2nd edn. Springer, Berlin","edition":"2"},{"key":"305_CR24","volume-title":"Self-validated numerical methods and applications. Brazilian mathematics colloquium monographs","author":"LH Figueiredo de","year":"1997","unstructured":"de Figueiredo LH, Stolfi J (1997) Self-validated numerical methods and applications. Brazilian mathematics colloquium monographs. IMPA\/CNPq, Rio de Janeiro"},{"key":"305_CR25","first-page":"79","volume":"22","author":"J Alexandre dit Sandretto","year":"2016","unstructured":"Alexandre dit Sandretto J, Chapoutot A (2016) Validated explicit and implicit Runge\u2013Kutta methods. Reliab Comput 22:79\u2013103","journal-title":"Reliab Comput"},{"key":"305_CR26","unstructured":"Lohner RJ (1987) Enclosing the solutions of ordinary initial and boundary value problems. In: Computer arithmetic, pp 255\u2013286"},{"issue":"2","key":"305_CR27","doi-asserted-by":"crossref","first-page":"365","DOI":"10.3934\/dcdsb.2009.11.365","volume":"11","author":"T Kapela","year":"2009","unstructured":"Kapela T, Zgliczynski P (2009) A Lohner-type algorithm for control systems and ordinary differential inclusions. Discrete Contin Dyn Syst Ser B 11(2):365\u2013385","journal-title":"Discrete Contin Dyn Syst Ser B"},{"key":"305_CR28","unstructured":"Alexandre dit Sandretto J, Chapoutot A (2015) DynIBEX library. http:\/\/perso.ensta-paristech.fr\/~chapoutot\/dynibex\/"},{"key":"305_CR29","doi-asserted-by":"crossref","unstructured":"Mazo M, Davitian A, Tabuada P (2010) PESSOA: a tool for embedded controller synthesis. In: Proceedings of computer aided verification, volume 6174 of LNCS, Springer, pp 566\u2013569","DOI":"10.1007\/978-3-642-14295-6_49"},{"key":"305_CR30","doi-asserted-by":"crossref","unstructured":"Rungger M, Zamani M (2016) SCOTS: a tool for the synthesis of symbolic controllers. In: ACM Proceedings of hybrid systems: computation and control, pp 99\u2013104","DOI":"10.1145\/2883817.2883834"},{"key":"305_CR31","doi-asserted-by":"crossref","unstructured":"Beccuti AG, Papafotiou G, Morari M (2005) Optimal control of the boost DC\u2013DC converter. In: IEEE Proceedings of conference on decision and control, pp 4457\u20134462","DOI":"10.1109\/CDC.2005.1582864"},{"issue":"7","key":"305_CR32","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1109\/TAC.2013.2246095","volume":"58","author":"J Liu","year":"2013","unstructured":"Liu J, Ozay N, Topcu U, Murray RM (2013) Synthesis of reactive switching protocols from temporal logic specifications. IEEE Trans Autom Control 58(7):1771\u20131785","journal-title":"IEEE Trans Autom Control"},{"key":"305_CR33","unstructured":"Meyer P-J (2015) Invariance and symbolic control of cooperative systems for temperature regulation in intelligent buildings. Theses, Universit\u00e9 Grenoble Alpes"},{"key":"305_CR34","doi-asserted-by":"crossref","unstructured":"Meyer P-J, Nazarpour H, Girard A, Witrant E (2014) Experimental implementation of UFAD regulation based on robust controlled invariance. In: IEEE Proceedings of European control conference, pp 1468\u20131473","DOI":"10.1109\/ECC.2014.6862273"},{"key":"305_CR35","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4gdk","volume-title":"Feedback systems: an introduction for scientists and engineers","author":"KJ Astr\u00f6m","year":"2010","unstructured":"Astr\u00f6m KJ, Murray RM (2010) Feedback systems: an introduction for scientists and engineers. Princeton University Press, Princeton"},{"key":"305_CR36","doi-asserted-by":"crossref","unstructured":"Le Co\u00ebnt A, Fribourg L, Markey N, de Vuyst F, Chamoin L (2016) Distributed synthesis of state-dependent switching control. In: Proceedings of reachability problems, volume 9899 of LNCS, Springer, pp 119\u2013133","DOI":"10.1007\/978-3-319-45994-3_9"},{"issue":"3","key":"305_CR37","doi-asserted-by":"crossref","first-page":"217","DOI":"10.3166\/ejc.18.217-238","volume":"18","author":"A Sangiovanni-Vincentelli","year":"2012","unstructured":"Sangiovanni-Vincentelli A, Damm W, Passerone R (2012) Taming Dr. Frankenstein: contract-based design for cyber-physical systems. Eur J Control 18(3):217\u2013238","journal-title":"Eur J Control"},{"key":"305_CR38","unstructured":"Le Co\u00ebnt A, de Vuyst F, Rey C, Chamoin L, Fribourg L (2016) Control of mechanical systems using set based methods. Int J Dyn Control 1\u201317"}],"container-title":["Formal Methods in System Design"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10703-017-0305-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10703-017-0305-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10703-017-0305-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,5]],"date-time":"2019-10-05T21:27:30Z","timestamp":1570310850000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10703-017-0305-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,11]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["305"],"URL":"https:\/\/doi.org\/10.1007\/s10703-017-0305-8","relation":{},"ISSN":["0925-9856","1572-8102"],"issn-type":[{"value":"0925-9856","type":"print"},{"value":"1572-8102","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,11]]}}}