{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:15:26Z","timestamp":1763468126024},"publisher-location":"Berlin, Heidelberg","reference-count":27,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642397981"},{"type":"electronic","value":"9783642397998"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-39799-8_20","type":"book-chapter","created":{"date-parts":[[2013,7,10]],"date-time":"2013-07-10T19:13:06Z","timestamp":1373483586000},"page":"280-295","source":"Crossref","is-referenced-by-count":21,"title":["Abstraction Based Model-Checking of Stability of Hybrid Systems"],"prefix":"10.1007","author":[{"given":"Pavithra","family":"Prabhakar","sequence":"first","affiliation":[]},{"given":"Miriam","family":"Garcia Soto","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"20_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1007\/3-540-36577-X_15","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"R. Alur","year":"2003","unstructured":"Alur, R., Dang, T., Ivan\u010di\u0107, F.: Counter-Example Guided Predicate Abstraction of Hybrid Systems. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol.\u00a02619, pp. 208\u2013223. Springer, Heidelberg (2003)"},{"issue":"7","key":"20_CR2","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s00236-006-0035-7","volume":"43","author":"E. Asarin","year":"2007","unstructured":"Asarin, E., Dang, T., Girard, A.: Hybridization methods for the analysis of nonlinear systems. Acta Informatica\u00a043(7), 451\u2013476 (2007)","journal-title":"Acta Informatica"},{"issue":"1","key":"20_CR3","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0304-3975(94)00228-B","volume":"138","author":"E. Asarin","year":"1995","unstructured":"Asarin, E., Maler, O., Pnueli, A.: Reachability analysis of dynamical systems having piecewise-constant derivatives. Theoretical Computer Science\u00a0138(1), 35\u201365 (1995)","journal-title":"Theoretical Computer Science"},{"key":"20_CR4","unstructured":"Branicky, M.S.: Stability of hybrid systems. In: Unbehauen, H. (ed.) Encylopedia of Life Support Systems. Control Sytems, Robotics and Automation, volume Theme 6.43, chapter Article 6.43.28.3. UNESCO Publishing (2004)"},{"key":"20_CR5","doi-asserted-by":"crossref","unstructured":"Chen, X., Abraham, E., Sankaranarayanan, S.: Taylor model flowpipe construction for non-linear hybrid systems. In: Proceedings of the IEEE Real-Time Systems Symposium (2012)","DOI":"10.1109\/RTSS.2012.70"},{"issue":"4","key":"20_CR6","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1142\/S012905410300190X","volume":"14","author":"E.M. Clarke","year":"2003","unstructured":"Clarke, E.M., Fehnker, A., Han, Z., Krogh, B., Ouaknine, J., Stursberg, O., Theobald, M.: Abstraction and Counterexample-Guided Refinement in Model Checking of Hybrid Systems. International Journal on Foundations of Computer Science\u00a014(4), 583\u2013604 (2003)","journal-title":"International Journal on Foundations of Computer Science"},{"key":"20_CR7","unstructured":"Davrazos, G., Koussoulas, N.T.: A review of stability results for switched and hybrid systems. In: Proceedings of the Mediterranean Conference on Control (2001)"},{"key":"20_CR8","doi-asserted-by":"crossref","unstructured":"Dierks, H., Kupferschmid, S., Larsen, K.G.: Automatic Abstraction Refinement for Timed Automata. In: Proceedings of Formal Modeling and Analysis of Timed Systems, pp. 114\u2013129 (2007)","DOI":"10.1007\/978-3-540-75454-1_10"},{"key":"20_CR9","doi-asserted-by":"crossref","unstructured":"Duggirala, P.S., Mitra, S.: Lyapunov abstractions for inevitability of hybrid systems. In: Proceedings of the International Conference on Hybrid Systems: Computation and Control, pp. 115\u2013124 (2012)","DOI":"10.1145\/2185632.2185652"},{"key":"20_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1007\/978-3-540-31954-2_17","volume-title":"Hybrid Systems: Computation and Control","author":"G. Frehse","year":"2005","unstructured":"Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past hytech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol.\u00a03414, pp. 258\u2013273. Springer, Heidelberg (2005)"},{"key":"20_CR11","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.\u00a03414, pp. 291\u2013305. Springer, Heidelberg (2005)"},{"key":"20_CR12","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/MCS.2008.931718","volume":"29","author":"R. Goebel","year":"2009","unstructured":"Goebel, R., Sanfelice, R., Teel, A.: Hybrid dynamical systems. IEEE Control Systems, Control Systems Magazine\u00a029, 28\u201393 (2009)","journal-title":"IEEE Control Systems, Control Systems Magazine"},{"key":"20_CR13","doi-asserted-by":"crossref","unstructured":"Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What\u2019s decidable about hybrid automata? In: Proceedings of the ACM Symposium on Theory of Computation, pp. 373\u2013382 (1995)","DOI":"10.1145\/225058.225162"},{"key":"20_CR14","unstructured":"Henzinger, T.A.: The Theory of Hybrid Automata. In: Proceedings of the IEEE Symposium on Logic in Computer Science, pp. 278\u2013292 (1996)"},{"key":"20_CR15","volume-title":"Nonlinear Systems","author":"H.K. Khalil","year":"1996","unstructured":"Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River (1996)"},{"key":"20_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0017-8","volume-title":"Switching in Systems and Control","author":"D. Liberzon","year":"2003","unstructured":"Liberzon, D.: Switching in Systems and Control. Birkhuser, Boston (2003)"},{"key":"20_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1007\/978-3-540-71493-4_74","volume-title":"Hybrid Systems: Computation and Control","author":"J. Oehlerking","year":"2007","unstructured":"Oehlerking, J., Burchardt, H., Theel, O.: Fully automated stability verification for piecewise affine systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol.\u00a04416, pp. 741\u2013745. Springer, Heidelberg (2007)"},{"key":"20_CR18","unstructured":"Parrilo, P.A.: Structure Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, Pasadena, CA (May 2000)"},{"key":"20_CR19","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/978-3-540-71070-7_15","volume-title":"Automated Reasoning","author":"A. Platzer","year":"2008","unstructured":"Platzer, A., Quesel, J.-D.: KeYmaera: A hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol.\u00a05195, pp. 171\u2013178. Springer, Heidelberg (2008)"},{"key":"20_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/11730637_38","volume-title":"Hybrid Systems: Computation and Control","author":"A. Podelski","year":"2006","unstructured":"Podelski, A., Wagner, S.: Model checking of hybrid systems: From reachability towards stability. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol.\u00a03927, pp. 507\u2013521. Springer, Heidelberg (2006)"},{"key":"20_CR21","doi-asserted-by":"crossref","unstructured":"Prabhakar, P., Vladimerou, V., Viswanathan, M., Dullerud, G.E.: Verifying tolerant systems using polynomial approximations. In: Proceedings of the IEEE Real-Time Systems Symposium, pp. 181\u2013190 (2009)","DOI":"10.1109\/RTSS.2009.28"},{"key":"20_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/978-3-642-35873-9_6","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"P. Prabhakar","year":"2013","unstructured":"Prabhakar, P., Duggirala, P.S., Mitra, S., Viswanathan, M.: Hybrid automata-based CEGAR for rectangular hybrid systems. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol.\u00a07737, pp. 48\u201367. Springer, Heidelberg (2013)"},{"key":"20_CR23","doi-asserted-by":"crossref","unstructured":"Prabhakar, P., Dullerud, G.E., Viswanathan, M.: Pre-orders for reasoning about stability. In: Proceedings of the International Conference on Hybrid Systems: Computation and Control, pp. 197\u2013206 (2012)","DOI":"10.1145\/2185632.2185662"},{"key":"20_CR24","doi-asserted-by":"crossref","unstructured":"Prabhakar, P., Viswanathan, M.: A dynamic algorithm for approximate flow computations. In: Proceedings of the International Conference on Hybrid Systems: Computation and Control, pp. 133\u2013143 (2010)","DOI":"10.1145\/1967701.1967722"},{"key":"20_CR25","doi-asserted-by":"crossref","unstructured":"Prabhakar, P., Viswanathan, M.: On the decidability of stability of hybrid systems. In: Proceedings of the International Conference on Hybrid Systems: Computation and Control (2013)","DOI":"10.1145\/2461328.2461339"},{"key":"20_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/978-3-540-24743-2_32","volume-title":"Hybrid Systems: Computation and Control","author":"S. Prajna","year":"2004","unstructured":"Prajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol.\u00a02993, pp. 477\u2013492. Springer, Heidelberg (2004)"},{"key":"20_CR27","doi-asserted-by":"crossref","unstructured":"Puri, A., Borkar, V.S., Varaiya, P.: \u03b5-approximation of differential inclusions. In: Proceedings of the International Conference on Hybrid Systems: Computation and Control, pp. 362\u2013376 (1995)","DOI":"10.1007\/BFb0020960"}],"container-title":["Lecture Notes in Computer Science","Computer Aided Verification"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-39799-8_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T14:42:09Z","timestamp":1557931329000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-39799-8_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642397981","9783642397998"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-39799-8_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}