{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T17:34:32Z","timestamp":1781976872492,"version":"3.54.5"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,10,30]],"date-time":"2017-10-30T00:00:00Z","timestamp":1509321600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,10,30]],"date-time":"2017-10-30T00:00:00Z","timestamp":1509321600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006961","name":"California Institute of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100006961","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002790","name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["1552668"],"award-info":[{"award-number":["1552668"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Event Dyn Syst"],"published-print":{"date-parts":[[2018,9]]},"DOI":"10.1007\/s10626-017-0262-9","type":"journal-article","created":{"date-parts":[[2017,10,30]],"date-time":"2017-10-30T05:54:38Z","timestamp":1509342878000},"page":"349-374","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Simulations and bisimulations for analysis of stability with respect to inputs of hybrid systems"],"prefix":"10.1007","volume":"28","author":[{"given":"Pavithra","family":"Prabhakar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard M.","family":"Murray","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,10,30]]},"reference":[{"issue":"3","key":"262_CR1","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1109\/9.989067","volume":"47","author":"D Angeli","year":"2002","unstructured":"Angeli D (2002) A Lyapunov approach to incremental stability properties. IEEE Trans Autom Control 47(3):410\u2013421","journal-title":"IEEE Trans Autom Control"},{"key":"262_CR2","volume-title":"Set-valued analysis","author":"JP Aubin","year":"1990","unstructured":"Aubin JP, Frankowska H (1990) Set-valued analysis. Birkhauser, Boston"},{"issue":"1","key":"262_CR3","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.sysconle.2008.07.009","volume":"58","author":"C Cai","year":"2009","unstructured":"Cai C, Teel AR (2009) Characterizations of input-to-state stability for hybrid systems. Syst Control Lett 58(1):47\u201353","journal-title":"Syst Control Lett"},{"key":"262_CR4","doi-asserted-by":"crossref","unstructured":"Caspi P, Benveniste A (2002) Toward an approximation theory for computerised control. In: EMSOFT, pp 294\u2013304","DOI":"10.1007\/3-540-45828-X_22"},{"key":"262_CR5","volume-title":"Model checking","author":"JrEM Clarke","year":"1999","unstructured":"Clarke JrE M, Grumberg O, Peled DA (1999) Model checking. MIT Press, Cambridge"},{"key":"262_CR6","doi-asserted-by":"crossref","unstructured":"Cuijpers PJL (2007) On bicontinuous bisimulation and the preservation of stability. In: HSCC, pp 676\u2013 679","DOI":"10.1007\/978-3-540-71493-4_59"},{"key":"262_CR7","doi-asserted-by":"crossref","unstructured":"Davoren JM (2009) Epsilon-tubes and generalized skorokhod metrics for hybrid paths spaces. In: HSCC, pp 135\u2013149","DOI":"10.1007\/978-3-642-00602-9_10"},{"issue":"1","key":"262_CR8","doi-asserted-by":"publisher","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"},{"key":"262_CR9","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCS.2008.931718","volume":"29","author":"R Goebel","year":"2009","unstructured":"Goebel R, Sanfelice R, Teel A (2009) Hybrid dynamical systems. IEEE Control Systems Magazine 29:28\u201393","journal-title":"IEEE Control Systems Magazine"},{"issue":"12","key":"262_CR10","doi-asserted-by":"publisher","first-page":"3079","DOI":"10.1016\/j.automatica.2008.04.025","volume":"44","author":"WPMH Heemels","year":"2008","unstructured":"Heemels WPMH, Weiland S (2008) Input-to-state stability and interconnections of discontinuous dynamical systems. Automatica 44(12):3079\u20133086","journal-title":"Automatica"},{"key":"262_CR11","doi-asserted-by":"crossref","unstructured":"Henzinger TA (1996) The theory of hybrid automata. In: LICS, pp 278\u2013292","DOI":"10.1109\/LICS.1996.561342"},{"key":"262_CR12","unstructured":"Hespanha JP, Morse AS (1999) Stability of switched systems with average dwell-time. In: IEEE CDC, pp 2655\u20132660"},{"issue":"11","key":"262_CR13","doi-asserted-by":"publisher","first-page":"2735","DOI":"10.1016\/j.automatica.2008.03.021","volume":"44","author":"JP Hespanha","year":"2008","unstructured":"Hespanha JP, Liberzon D, Teel AR (2008) Lyapunov conditions for input-to-state stability of impulsive systems. Automatica 44(11):2735\u20132744","journal-title":"Automatica"},{"key":"262_CR14","doi-asserted-by":"crossref","unstructured":"Kaynar DK, Lynch NA, Segala R, Vaandrager FW (2003) Timed I\/O automata: a mathematical framework for modeling and analyzing real-time systems. In: IEEE RTSS, pp 166\u2013177","DOI":"10.1109\/REAL.2003.1253264"},{"key":"262_CR15","volume-title":"Nonlinear systems","author":"HK Khalil","year":"1996","unstructured":"Khalil HK (1996) Nonlinear systems. Prentice-Hall Inc, Upper Saddle River"},{"key":"262_CR16","doi-asserted-by":"crossref","unstructured":"Lee D, Yannakakis M (1992) Online minimization of transition systems (extended abstract). In: STOC, pp 264\u2013274","DOI":"10.1145\/129712.129738"},{"key":"262_CR17","doi-asserted-by":"crossref","unstructured":"Li Y, Sanfelice RG (2015) On necessary and sufficient conditions for incremental stability of hybrid systems using the graphical distance between solutions. In: IEEE CDC, pp 5575\u20135580","DOI":"10.1109\/CDC.2015.7403093"},{"key":"262_CR18","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1016\/j.sysconle.2012.03.007","volume":"61","author":"J Liu","year":"2012","unstructured":"Liu J, Liu X, Xie WC (2012) Class-kl estimates and input-to-state stability analysis of impulsive switched systems. Syst. Control Lett. 61:738\u2013746","journal-title":"Syst. Control Lett."},{"key":"262_CR19","volume-title":"Communication and concurrency","author":"R Milner","year":"1989","unstructured":"Milner R (1989) Communication and concurrency. Prentice-Hall, Inc, Upper Saddle River"},{"issue":"9","key":"262_CR20","doi-asserted-by":"publisher","first-page":"2029","DOI":"10.1016\/j.automatica.2012.06.026","volume":"48","author":"MA M\u00fcller","year":"2012","unstructured":"M\u00fcller MA, Liberzon D (2012) Input\/output-to-state stability and state-norm estimators for switched nonlinear systems. Automatica 48(9):2029\u20132039","journal-title":"Automatica"},{"key":"262_CR21","doi-asserted-by":"crossref","unstructured":"Papachristodoulou A, Prajna S (2002) On the construction of Lyapunov functions using the sum of squares decomposition. In: IEEE CDC, pp 3482\u20133487","DOI":"10.1109\/CDC.2002.1184414"},{"key":"262_CR22","unstructured":"Parrilo PA (2000) Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Doctoral dissertation, California Institute of Technology"},{"key":"262_CR23","doi-asserted-by":"crossref","unstructured":"Postoyan R, Biemond J, Heemels W, Van de Wouw N (2015) Definitions of incremental stability for hybrid systems. In: IEEE CDC, pp 5544\u20135549","DOI":"10.1109\/CDC.2015.7403088"},{"key":"262_CR24","doi-asserted-by":"crossref","unstructured":"Prabhakar P, Soto MG (2013) Abstraction based model-checking of stability of hybrid systems. In: CAV, pp 280\u2013295","DOI":"10.1007\/978-3-642-39799-8_20"},{"key":"262_CR25","doi-asserted-by":"crossref","unstructured":"Prabhakar P, Dullerud GE, Viswanathan M (2012) Pre-orders for reasoning about stability. In: HSCC, pp 197\u2013206","DOI":"10.1145\/2185632.2185662"},{"key":"262_CR26","doi-asserted-by":"crossref","unstructured":"Prabhakar P, Liu J, Murray RM (2013) Pre-orders for reasoning about stability properties with respect to input of hybrid systems. In: EMSOFT, pp 1\u201310","DOI":"10.1109\/EMSOFT.2013.6658602"},{"issue":"5","key":"262_CR27","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/0167-6911(94)00050-6","volume":"24","author":"E Sontag","year":"1995","unstructured":"Sontag E, Wang Y (1995) On characterizations of the input-to-state stability property. Syst. Control Lett. 24(5):351\u2013359","journal-title":"Syst. Control Lett."},{"key":"262_CR28","unstructured":"Sontag ED (2006) Input to state stability: Basic concepts and results. In: Nonlinear and Optimal control Theory. Springer, Berlin, pp 163\u2013220"},{"key":"262_CR29","doi-asserted-by":"crossref","unstructured":"Tabuada P, Balkan A, Caliskan SY, Shoukry Y, Majumdar R (2012) Input-output robustness for discrete systems. In: EMSOFT, pp 217\u2013226","DOI":"10.1145\/2380356.2380396"},{"issue":"4","key":"262_CR30","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1016\/j.automatica.2006.10.007","volume":"43","author":"L Vu","year":"2007","unstructured":"Vu L, Chatterjee D, Liberzon D (2007) Input-to-state stability of switched systems and switching adaptive control. Automatica 43(4):639\u2013646","journal-title":"Automatica"}],"container-title":["Discrete Event Dynamic Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10626-017-0262-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-017-0262-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-017-0262-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T15:03:27Z","timestamp":1589727807000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10626-017-0262-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,30]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["262"],"URL":"https:\/\/doi.org\/10.1007\/s10626-017-0262-9","relation":{},"ISSN":["0924-6703","1573-7594"],"issn-type":[{"value":"0924-6703","type":"print"},{"value":"1573-7594","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,30]]},"assertion":[{"value":"16 February 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}