{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T18:32:13Z","timestamp":1781893933552,"version":"3.54.5"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540212591","type":"print"},{"value":"9783540247432","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-24743-2_32","type":"book-chapter","created":{"date-parts":[[2010,8,2]],"date-time":"2010-08-02T15:02:22Z","timestamp":1280761342000},"page":"477-492","source":"Crossref","is-referenced-by-count":450,"title":["Safety Verification of Hybrid Systems Using Barrier Certificates"],"prefix":"10.1007","author":[{"given":"Stephen","family":"Prajna","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Jadbabaie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"32_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/0304-3975(94)00202-T","volume":"138","author":"R. Alur","year":"1995","unstructured":"Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Oliviero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science\u00a0138, 3\u201334 (1995)","journal-title":"Theoretical Computer Science"},{"key":"32_CR2","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":"32_CR3","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":"32_CR4","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":"32_CR5","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":"32_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/3-540-46430-1_10","volume-title":"Hybrid Systems: Computation and Control","author":"O. Botchkarev","year":"2000","unstructured":"Botchkarev, O., Tripakis, S.: Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol.\u00a01790, pp. 73\u201388. Springer, Heidelberg (2000)"},{"key":"32_CR7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970777","volume-title":"Linear Matrix Inequalities in System and Control Theory","author":"S. Boyd","year":"1994","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)"},{"issue":"4","key":"32_CR8","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1109\/9.664150","volume":"43","author":"M.S. Branicky","year":"1998","unstructured":"Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automatic Control\u00a043(4), 475\u2013482 (1998)","journal-title":"IEEE Trans. Automatic Control"},{"issue":"1","key":"32_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 Trans. Automatic Control\u00a048(1), 64\u201375 (2003)","journal-title":"IEEE Trans. Automatic Control"},{"issue":"6","key":"32_CR10","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1109\/6.499951","volume":"33","author":"E.M. Clarke","year":"1996","unstructured":"Clarke, E.M., Kurshan, R.P.: Computer-aided verification. IEEE Spectrum\u00a033(6), 61\u201367 (1996)","journal-title":"IEEE Spectrum"},{"issue":"4","key":"32_CR11","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1109\/9.664157","volume":"43","author":"M. Johansson","year":"1998","unstructured":"Johansson, M., Rantzer, A.: Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Automat. Control\u00a043(4), 555\u2013559 (1998)","journal-title":"IEEE Trans. Automat. Control"},{"key":"32_CR12","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":"32_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/3-540-46430-1_19","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)"},{"issue":"3","key":"32_CR14","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. J. Symbolic Computation\u00a032(3), 231\u2013253 (2001)","journal-title":"J. Symbolic Computation"},{"issue":"6","key":"32_CR15","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1109\/9.587335","volume":"42","author":"A. Megretski","year":"1997","unstructured":"Megretski, A., Rantzer, A.: System analysis via integral quadratic constraints. IEEE Trans. Automatic Control\u00a042(6), 819\u2013830 (1997)","journal-title":"IEEE Trans. Automatic Control"},{"key":"32_CR16","volume-title":"Control in an Information Rich World: Report of the Panel on Future Directions in Control, Dynamics, and Systems","year":"2003","unstructured":"Murray, R.M. (ed.): Control in an Information Rich World: Report of the Panel on Future Directions in Control, Dynamics, and Systems. SIAM, Philadelphia (2003), Available at http:\/\/www.cds.caltech.edu\/~murray\/cdspanel"},{"key":"32_CR17","unstructured":"Papachristodoulou, A., Prajna, S.: On the construction of Lyapunov functions using the sum of squares decomposition. In: Proceedings IEEE CDC (2002)"},{"key":"32_CR18","unstructured":"Parrilo, P.A.: Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, Caltech, Pasadena, CA (2000)"},{"key":"32_CR19","unstructured":"Prajna, S.: Barrier certificates for nonlinear model validation. In: Proceedings IEEE Conference on Decision and Control (2003)"},{"key":"32_CR20","unstructured":"Prajna, S., Papachristodoulou, A., Parrilo, P.A.: Introducing SOSTOOLS: A general purpose sum of squares programming solver. In: Proceedings IEEE CDC (2002), Available at http:\/\/www.cds.caltech.edu\/sostools and http:\/\/www.aut.ee.ethz.ch\/~parrilo\/sostools"},{"issue":"6","key":"32_CR21","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1007\/BF01070233","volume":"23","author":"N.Z. Shor","year":"1987","unstructured":"Shor, N.Z.: Class of global minimum bounds of polynomial functions. Cybernetics\u00a023(6), 731\u2013734 (1987)","journal-title":"Cybernetics"},{"key":"32_CR22","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)"},{"issue":"7","key":"32_CR23","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. Proc. of the IEEE\u00a091(7), 986\u20131001 (2003)","journal-title":"Proc. of the IEEE"},{"issue":"1","key":"32_CR24","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L. Vandenberghe","year":"1996","unstructured":"Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review\u00a038(1), 49\u201395 (1996)","journal-title":"SIAM Review"},{"key":"32_CR25","doi-asserted-by":"crossref","unstructured":"Yazarel, H., Pappas, G.: Geometric programming relaxations for linear systems reachability. Submitted to the American Control Conference (2004)","DOI":"10.23919\/ACC.2004.1383661"},{"key":"32_CR26","volume-title":"Robust and Optimal Control","author":"K. Zhou","year":"1996","unstructured":"Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice-Hall, Inc., Upper Saddle River (1996)"}],"container-title":["Lecture Notes in Computer Science","Hybrid Systems: Computation and Control"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-24743-2_32","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T03:19:39Z","timestamp":1559359179000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-24743-2_32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004]]},"ISBN":["9783540212591","9783540247432"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-24743-2_32","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004]]}}}