{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:13:31Z","timestamp":1763468011209},"publisher-location":"Berlin, Heidelberg","reference-count":29,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540251088"},{"type":"electronic","value":"9783540319542"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/978-3-540-31954-2_35","type":"book-chapter","created":{"date-parts":[[2011,1,14]],"date-time":"2011-01-14T02:45:07Z","timestamp":1294973107000},"page":"542-556","source":"Crossref","is-referenced-by-count":17,"title":["Primal\u2013Dual Tests for Safety and Reachability"],"prefix":"10.1007","author":[{"given":"Stephen","family":"Prajna","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anders","family":"Rantzer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"35_CR1","volume-title":"Model Checking","author":"E.M. Clarke Jr.","year":"2000","unstructured":"Clarke Jr., E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)"},{"key":"35_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/3-540-46430-1_8","volume-title":"Hybrid Systems: Computation and Control","author":"A. Bemporad","year":"2000","unstructured":"Bemporad, A., Torrisi, F.D., Morari, M.: Optimization-based verification and stability characterization of piecewise affine and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol.\u00a01790, pp. 45\u201358. Springer, Heidelberg (2000)"},{"key":"35_CR3","series-title":"Lecture Notes in Computer Science","first-page":"203","volume-title":"Hybrid Systems: Computation and Control","author":"A. Kurzhanski","year":"2000","unstructured":"Kurzhanski, A., Varaiya, P.: Ellipsoidal techniques for reachability analysis. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol.\u00a01790, pp. 203\u2013213. Springer, Heidelberg (2000)"},{"key":"35_CR4","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1006\/jsco.2001.0472","volume":"32","author":"G. Lafferriere","year":"2001","unstructured":"Lafferriere, G., Pappas, G.J., Yovine, S.: Symbolic reachability computations for families of linear vector fields. Journal of Symbolic Computation\u00a032, 231\u2013253 (2001)","journal-title":"Journal of Symbolic Computation"},{"key":"35_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/3-540-45351-2_9","volume-title":"Hybrid Systems: Computation and Control","author":"H. Anai","year":"2001","unstructured":"Anai, H., Weispfenning, V.: Reach set computations using real quantifier elimination. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol.\u00a02034, pp. 63\u201376. Springer, Heidelberg (2001)"},{"key":"35_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/3-540-45657-0_30","volume-title":"Computer Aided Verification","author":"E. Asarin","year":"2002","unstructured":"Asarin, E., Dang, T., Maler, O.: The d\/dt tool for verification of hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol.\u00a02404, pp. 365\u2013370. Springer, Heidelberg (2002)"},{"key":"35_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1007\/3-540-36580-X_4","volume-title":"Hybrid Systems: Computation and Control","author":"R. Alur","year":"2003","unstructured":"Alur, R., Dang, T., Ivancic, F.: Progress on reachability analysis of hybrid systems using predicate abstraction. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol.\u00a02623, pp. 4\u201319. Springer, Heidelberg (2003)"},{"key":"35_CR8","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1109\/JPROC.2003.814621","volume":"91","author":"C.J. Tomlin","year":"2003","unstructured":"Tomlin, C.J., Mitchell, I., Bayen, A.M., Oishi, M.: Computational techniques for the verification of hybrid systems. Proceedings of the IEEE\u00a091, 986\u20131001 (2003)","journal-title":"Proceedings of the IEEE"},{"key":"35_CR9","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1109\/TAC.2002.806655","volume":"48","author":"A. Chutinan","year":"2003","unstructured":"Chutinan, A., Krogh, B.H.: Computational techniques for hybrid system verification. IEEE Transactions on Automatic Control\u00a048, 64\u201375 (2003)","journal-title":"IEEE Transactions on Automatic Control"},{"key":"35_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1007\/3-540-36580-X_37","volume-title":"Hybrid Systems: Computation and Control","author":"A. Tiwari","year":"2003","unstructured":"Tiwari, A.: Approximate reachability for linear systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol.\u00a02623, pp. 514\u2013525. Springer, Heidelberg (2003)"},{"key":"35_CR11","doi-asserted-by":"crossref","unstructured":"Yazarel, H., Pappas, G.: Geometric programming relaxations for linear systems reachability. In: Proceedings of the American Control Conference (2004)","DOI":"10.23919\/ACC.2004.1383661"},{"key":"35_CR12","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":"35_CR13","volume-title":"Nonlinear Systems","author":"H.K. Khalil","year":"1996","unstructured":"Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice-Hall, Inc., Upper Saddle River (1996)","edition":"2"},{"key":"35_CR14","unstructured":"Aubin, J.P.: Viability Theory. Birkh\u00e4user, Boston (1991)"},{"key":"35_CR15","doi-asserted-by":"crossref","unstructured":"Jirstrand, M.: Invariant sets for a class of hybrid systems. In: Proceedings of the IEEE Conference on Decision and Control (1998)","DOI":"10.1109\/CDC.1998.761784"},{"key":"35_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/978-3-540-24743-2_36","volume-title":"Hybrid Systems: Computation and Control","author":"S. Sankaranarayanan","year":"2004","unstructured":"Sankaranarayanan, S., Sipma, H., Manna, Z.: Constructing invariants for hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol.\u00a02993, pp. 539\u2013554. Springer, Heidelberg (2004)"},{"key":"35_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1007\/978-3-540-24743-2_40","volume-title":"Hybrid Systems: Computation and Control","author":"A. Tiwari","year":"2004","unstructured":"Tiwari, A., Khanna, G.: Nonlinear systems: Approximating reach sets. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol.\u00a02993, pp. 600\u2013614. Springer, Heidelberg (2004)"},{"key":"35_CR18","unstructured":"Parrilo, P.A.: Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, Pasadena, CA (2000)"},{"key":"35_CR19","unstructured":"Prajna, S., Papachristodoulou, A., Parrilo, P.A.: Introducing SOSTOOLS: A general purpose sum of squares programming solver. In: Proceedings of the IEEE Conference on Decision and Control (2002), Available at: \n                    \n                      http:\/\/www.cds.caltech.edu\/sostools\n                    \n                    \n                  , \n                    \n                      http:\/\/www.aut.ee.ethz.ch\/~parrilo\/sostools"},{"key":"35_CR20","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S. Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"35_CR21","doi-asserted-by":"crossref","unstructured":"Prajna, S., Jadbabaie, A., Pappas, G.J.: Stochastic safety verification using barrier certificates. In: Proceedings of the IEEE Conference on Decision and Control (2004)","DOI":"10.1109\/CDC.2004.1428804"},{"key":"35_CR22","unstructured":"Glavaski, S., Papachristodoulou, A., Ariyur, K.: Controlled hybrid system safety verification: Advanced life support system testbed (2005) (Submitted)"},{"key":"35_CR23","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1109\/5.871304","volume":"88","author":"R. Alur","year":"2000","unstructured":"Alur, R., Henzinger, T., Lafferriere, G., Pappas, G.J.: Discrete abstractions of hybrid systems. Proceedings of the IEEE\u00a088, 971\u2013984 (2000)","journal-title":"Proceedings of the IEEE"},{"key":"35_CR24","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0167-6911(00)00087-6","volume":"42","author":"A. Rantzer","year":"2001","unstructured":"Rantzer, A.: A dual to Lyapunov\u2019s stability theorem. Systems and Control Letters\u00a042, 161\u2013168 (2001)","journal-title":"Systems and Control Letters"},{"key":"35_CR25","doi-asserted-by":"crossref","unstructured":"Rantzer, A., Hedlund, S.: Duality between cost and density in optimal control. In: Proceedings of the IEEE Conference on Decision and Control (2003)","DOI":"10.1109\/CDC.2003.1272774"},{"key":"35_CR26","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"C.H. Papadimitriou","year":"1998","unstructured":"Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications Inc., Mineola (1998)"},{"key":"35_CR27","doi-asserted-by":"crossref","unstructured":"Prajna, S., Rantzer, A.: On the necessity of barrier certificates. In: Proceedings of the IFAC World Congress (2005) (to appear)","DOI":"10.3182\/20050703-6-CZ-1902.00743"},{"key":"35_CR28","unstructured":"Rantzer, A., Prajna, S.: On analysis and synthesis of safe control laws. In: Proceedings of the Allerton Conference on Communication, Control, and Computing (2004)"},{"key":"35_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0931-7","volume-title":"The Temporal Logic of Reactive and Concurrent Systems: Specification","author":"Z. Manna","year":"1992","unstructured":"Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, New York (1992)"}],"container-title":["Lecture Notes in Computer Science","Hybrid Systems: Computation and Control"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-31954-2_35.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T23:43:11Z","timestamp":1619998991000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-31954-2_35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540251088","9783540319542"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-31954-2_35","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}