{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T12:42:31Z","timestamp":1773319351604,"version":"3.50.1"},"publisher-location":"Cham","reference-count":35,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030296612","type":"print"},{"value":"9783030296629","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-29662-9_10","type":"book-chapter","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T19:03:06Z","timestamp":1566241386000},"page":"160-177","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Reachability Analysis for High-Index Linear Differential Algebraic Equations"],"prefix":"10.1007","author":[{"given":"Hoang-Dung","family":"Tran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luan Viet","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nathaniel","family":"Hamilton","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9065-8428","authenticated-orcid":false,"given":"Weiming","family":"Xiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8021-9923","authenticated-orcid":false,"given":"Taylor T.","family":"Johnson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"issue":"2","key":"10_CR1","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1109\/TAC.2013.2285751","volume":"59","author":"M Althoff","year":"2014","unstructured":"Althoff, M., Krogh, B.: Reachability analysis of nonlinear differential-algebraic systems. IEEE Trans. Autom. Control 59(2), 371\u2013383 (2014). https:\/\/doi.org\/10.1109\/TAC.2013.2285751","journal-title":"IEEE Trans. Autom. Control"},{"key":"10_CR2","unstructured":"Althoff, M.: An introduction to CORA 2015. In: Proceedings of the Workshop on Applied Verification for Continuous and Hybrid Systems (2015)"},{"issue":"1","key":"10_CR3","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s10009-017-0458-1","volume":"21","author":"S Bak","year":"2019","unstructured":"Bak, S., Beg, O.A., Bogomolov, S., Johnson, T.T., Nguyen, L.V., Schilling, C.: Hybrid automata: from verification to implementation. Int. J. Softw. Tools Technol. Transf. 21(1), 87\u2013104 (2019). https:\/\/doi.org\/10.1007\/s10009-017-0458-1","journal-title":"Int. J. Softw. Tools Technol. Transf."},{"key":"10_CR4","doi-asserted-by":"crossref","unstructured":"Bak, S., Bogomolov, S., Johnson, T.T.: HYST: a source transformation and translation tool for hybrid automaton models. In: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, pp. 128\u2013133. ACM (2015)","DOI":"10.1145\/2728606.2728630"},{"key":"10_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/978-3-319-63387-9_20","volume-title":"Computer Aided Verification","author":"S Bak","year":"2017","unstructured":"Bak, S., Duggirala, P.S.: Simulation-equivalent reachability of large linear systems with inputs. In: Majumdar, R., Kun\u010dak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 401\u2013420. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63387-9_20"},{"key":"10_CR6","doi-asserted-by":"publisher","unstructured":"Bak, S., Tran, H.D., Johnson, T.T.: Numerical verification of affine systems with up to a billion dimensions. In: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019, pp. 23\u201332. ACM, New York (2019). https:\/\/doi.org\/10.1145\/3302504.3311792","DOI":"10.1145\/3302504.3311792"},{"key":"10_CR7","doi-asserted-by":"publisher","DOI":"10.2991\/978-94-6239-189-5","volume-title":"Index-Aware Model Order Reduction Methods","author":"N Banagaaya","year":"2016","unstructured":"Banagaaya, N., Al\u00ec, G., Schilders, W.H.: Index-Aware Model Order Reduction Methods. Springer, Cham (2016). https:\/\/doi.org\/10.2991\/978-94-6239-189-5"},{"issue":"5","key":"10_CR8","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/0098-1354(88)85052-X","volume":"12","author":"G Byrne","year":"1988","unstructured":"Byrne, G., Ponzi, P.: Differential-algebraic systems, their applications and solutions. Comput. Chem. Eng. 12(5), 377\u2013382 (1988)","journal-title":"Comput. Chem. Eng."},{"key":"10_CR9","unstructured":"Chahlaoui, Y., Van Dooren, P.: A collection of benchmark examples for model reduction of linear time invariant dynamical systems (2002)"},{"key":"10_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1007\/978-3-642-39799-8_18","volume-title":"Computer Aided Verification","author":"X Chen","year":"2013","unstructured":"Chen, X., \u00c1brah\u00e1m, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258\u2013263. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39799-8_18"},{"key":"10_CR11","doi-asserted-by":"crossref","unstructured":"Cross, E.A., Mitchell, I.M.: Level set methods for computing reachable sets of systems with differential algebraic equation dynamics. In: American Control Conference, pp. 2260\u20132265. IEEE (2008)","DOI":"10.1109\/ACC.2008.4586828"},{"key":"10_CR12","series-title":"Lecture Notes in Control and Information Sciences","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0002475","volume-title":"Singular Control Systems","author":"L Dai","year":"1989","unstructured":"Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer, Heidelberg (1989)"},{"key":"10_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-3-540-30494-4_3","volume-title":"Formal Methods in Computer-Aided Design","author":"T Dang","year":"2004","unstructured":"Dang, T., Donz\u00e9, A., Maler, O.: Verification of analog and mixed-signal circuits using hybrid system techniques. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 21\u201336. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-30494-4_3"},{"key":"10_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-6397-0","volume-title":"Analysis and Design of Descriptor Linear Systems","author":"GR Duan","year":"2010","unstructured":"Duan, G.R.: Analysis and Design of Descriptor Linear Systems, vol. 23. Springer, New York (2010)"},{"key":"10_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1007\/978-3-662-46681-0_5","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"PS Duggirala","year":"2015","unstructured":"Duggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2E2: a verification tool for stateflow models. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 68\u201382. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-46681-0_5"},{"key":"10_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/978-3-319-41528-4_26","volume-title":"Computer Aided Verification","author":"PS Duggirala","year":"2016","unstructured":"Duggirala, P.S., Viswanathan, M.: Parsimonious, simulation based verification of linear systems. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 477\u2013494. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-41528-4_26"},{"key":"10_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-09828-7","volume-title":"Numerical Methods in Multibody Dynamics","author":"E Eich-Soellner","year":"1998","unstructured":"Eich-Soellner, E., F\u00fchrer, C.: Numerical Methods in Multibody Dynamics, vol. 45. Springer, Wiesbaden (1998). https:\/\/doi.org\/10.1007\/978-3-663-09828-7"},{"key":"10_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/978-3-319-41528-4_29","volume-title":"Computer Aided Verification","author":"C Fan","year":"2016","unstructured":"Fan, C., Qi, B., Mitra, S., Viswanathan, M., Duggirala, P.S.: Automatic reachability analysis for nonlinear hybrid models with C2E2. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 531\u2013538. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-41528-4_29"},{"key":"10_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/978-3-642-22110-1_30","volume-title":"Computer Aided Verification","author":"G Frehse","year":"2011","unstructured":"Frehse, G., et al.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379\u2013395. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22110-1_30"},{"key":"10_CR20","unstructured":"Gerdin, M.: Parameter estimation in linear descriptor systems. Citeseer (2004)"},{"key":"10_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/978-3-540-31954-2_19","volume-title":"Hybrid Systems: Computation and Control","author":"A Girard","year":"2005","unstructured":"Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291\u2013305. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/978-3-540-31954-2_19"},{"issue":"2","key":"10_CR22","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/j.nahs.2009.03.002","volume":"4","author":"CL Guernic","year":"2010","unstructured":"Guernic, C.L., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Anal. Hybrid Syst. 4(2), 250\u2013262 (2010). https:\/\/doi.org\/10.1016\/j.nahs.2009.03.002","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"10_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/11730637_23","volume-title":"Hybrid Systems: Computation and Control","author":"Z Han","year":"2006","unstructured":"Han, Z., Krogh, B.H.: Reachability analysis of large-scale affine systems using low-dimensional polytopes. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 287\u2013301. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11730637_23"},{"issue":"6","key":"10_CR24","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1109\/TCS.1975.1084079","volume":"22","author":"CW Ho","year":"1975","unstructured":"Ho, C.W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. 22(6), 504\u2013509 (1975)","journal-title":"IEEE Trans. Circuits Syst."},{"key":"10_CR25","doi-asserted-by":"crossref","unstructured":"Kong, S., Gao, S., Chen, W., Clarke, E.: dreach: $$\\delta $$ -reachability analysis for hybrid systems, pp. 200\u2013205 (2015)","DOI":"10.1007\/978-3-662-46681-0_15"},{"issue":"4\u20135","key":"10_CR26","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0898-1221(95)00224-3","volume":"31","author":"R M\u00e4rz","year":"1996","unstructured":"M\u00e4rz, R.: Canonical projectors for linear differential algebraic equations. Comput. Math. Appl. 31(4\u20135), 121\u2013135 (1996)","journal-title":"Comput. Math. Appl."},{"key":"10_CR27","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/3-540-27909-1_3","volume-title":"Dimension Reduction of Large-Scale Systems","author":"V Mehrmann","year":"2005","unstructured":"Mehrmann, V., Stykel, T.: Balanced truncation model reduction for large-scale systems in descriptor form. In: Benner, P., Sorensen, D.C., Mehrmann, V. (eds.) Dimension Reduction of Large-Scale Systems. LNCSE, vol. 45, pp. 83\u2013115. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/3-540-27909-1_3"},{"key":"10_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1007\/978-3-540-78929-1_51","volume-title":"Hybrid Systems: Computation and Control","author":"IM Mitchell","year":"2008","unstructured":"Mitchell, I.M., Susuki, Y.: Level set methods for computing reachable sets of hybrid systems with differential algebraic equation dynamics. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 630\u2013633. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-78929-1_51"},{"key":"10_CR29","doi-asserted-by":"publisher","first-page":"174","DOI":"10.29007\/4gj7","volume":"54","author":"P Musau","year":"2018","unstructured":"Musau, P., Lopez, D.M., Tran, H.D., Johnson, T.T.: Linear differential-algebraic equations (benchmark proposal). EPiC Ser. Comput. 54, 174\u2013184 (2018)","journal-title":"EPiC Ser. Comput."},{"key":"10_CR30","unstructured":"Schon, T., Gerdin, M., Glad, T., Gustafsson, F.: A modeling and filtering framework for linear differential-algebraic equations. In: 42nd IEEE Conference on Decision and Control. Proceedings, vol. 1, pp. 892\u2013897. IEEE (2003)"},{"key":"10_CR31","doi-asserted-by":"publisher","first-page":"185","DOI":"10.29007\/fvpp","volume":"54","author":"HD Tran","year":"2018","unstructured":"Tran, H.D., Bao, T., Johnson, T.T.: Discrete-space analysis of partial differential equations. EPiC Seri. Comput. 54, 185\u2013195 (2018)","journal-title":"EPiC Seri. Comput."},{"key":"10_CR32","doi-asserted-by":"crossref","unstructured":"Tran, H.D., Nguyen, L.V., Hamilton, N., Xiang, W., Johnson, T.T.: Reachability analysis for high-index linear differential algebraic equations: extended version. In: 17th International Conference on Formal Modeling and Analysis of Timed Systems (2019)","DOI":"10.1007\/978-3-030-29662-9_10"},{"key":"10_CR33","unstructured":"Tran, H.D., Nguyen, L.V., Johnson, T.T.: Large-scale linear systems from order-reduction (benchmark proposal). In: 3rd Applied Verification for Continuous and Hybrid Systems Workshop (ARCH), Vienna, Austria (2016)"},{"issue":"2","key":"10_CR34","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/s10626-017-0244-y","volume":"27","author":"HD Tran","year":"2017","unstructured":"Tran, H.D., Nguyen, L.V., Xiang, W., Johnson, T.T.: Order-reduction abstractions for safety verification of high-dimensional linear systems. Discrete Event Dyn. Syst. 27(2), 443\u2013461 (2017)","journal-title":"Discrete Event Dyn. Syst."},{"issue":"16","key":"10_CR35","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.ifacol.2018.08.023","volume":"51","author":"HD Tran","year":"2018","unstructured":"Tran, H.D., Xiang, W., Bak, S., Johnson, T.T.: Reachability analysis for one dimensional linear parabolic equations. IFAC-PapersOnLine 51(16), 133\u2013138 (2018)","journal-title":"IFAC-PapersOnLine"}],"container-title":["Lecture Notes in Computer Science","Formal Modeling and Analysis of Timed Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-29662-9_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T14:46:50Z","timestamp":1575557210000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-29662-9_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030296612","9783030296629"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-29662-9_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"13 August 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FORMATS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Formal Modeling and Analysis of Timed Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Amsterdam","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 August 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 August 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"formats2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/lipn.univ-paris13.fr\/formats2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"42","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"15","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"36% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.1","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4.4","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}