Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems, pp.209-229, 1992. ,
DOI : 10.1007/3-540-57318-6_30
Progress on Reachability Analysis of Hybrid Systems Using Predicate Abstraction, In: HSCC. pp, pp.4-19, 2003. ,
DOI : 10.1007/3-540-36580-X_4
Predicate abstraction for reachability analysis of hybrid systems, ACM Transactions on Embedded Computing Systems, vol.5, issue.1, pp.152-199, 2006. ,
DOI : 10.1145/1132357.1132363
Dynamical systems. Differential equations, maps and chaotic behaviour, 1992. ,
Set invariance in control, Automatica, vol.35, issue.11, pp.1747-1767, 1999. ,
DOI : 10.1016/S0005-1098(99)00113-2
Qualitative Theory of Planar Differential Systems, 2006. ,
Characterizing Algebraic Invariants by Differential Radical Invariants, pp.279-294, 2014. ,
DOI : 10.1007/978-3-642-54862-8_19
A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets, pp.431-448, 2015. ,
DOI : 10.1007/978-3-662-46081-8_24
Integrability and Nonintegrability of Dynamical Systems Advanced series in nonlinear dynamics, World Scientific, 2001. ,
Constraint-Based Approach for Analysis of Hybrid Systems, LNCS, vol.5123, pp.190-203, 2008. ,
DOI : 10.1007/978-3-540-70545-1_18
Differential Equations: Linearity vs. Nonlinearity, SIAM Review, vol.5, issue.3, pp.249-272, 1963. ,
DOI : 10.1137/1005068
The theory of hybrid automata, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science, pp.278-292, 1996. ,
DOI : 10.1109/LICS.1996.561342
Computing semi-algebraic invariants for polynomial dynamical systems, Proceedings of the ninth ACM international conference on Embedded software, EMSOFT '11, pp.97-106, 2011. ,
DOI : 10.1145/2038642.2038659
Abstraction of Elementary Hybrid Systems by Variable Transformation, FM 2015, pp.360-377, 2015. ,
DOI : 10.1007/978-3-319-19249-9_23
Generating Invariants for Non-linear Hybrid Systems by Linear Algebraic Methods, ) SAS. LNCS, pp.373-389, 2010. ,
DOI : 10.1007/978-3-642-15769-1_23
Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition, Positive Polynomials in Control, pp.23-43, 2005. ,
DOI : 10.1007/10997703_2
Differential Dynamic Logic for Hybrid Systems, Journal of Automated Reasoning, vol.30, issue.1, pp.143-189, 2008. ,
DOI : 10.1007/s10817-008-9103-8
Differential-algebraic Dynamic Logic for Differential-algebraic Programs, Journal of Logic and Computation, vol.20, issue.1, pp.309-352, 2010. ,
DOI : 10.1093/logcom/exn070
The Complete Proof Theory of Hybrid Systems, 2012 27th Annual IEEE Symposium on Logic in Computer Science, pp.541-550, 2012. ,
DOI : 10.1109/LICS.2012.64
The Structure of Differential Invariants and Differential Cut Elimination, Logical Methods in Computer Science, vol.8, issue.4, pp.1-38, 2012. ,
DOI : 10.2168/LMCS-8(4:16)2012
Computing differential invariants of hybrid systems as fixedpoints, pp.176-189, 2008. ,
Elimination of special functions from differential equations, Communications of the ACM, vol.2, issue.3, pp.3-4, 1959. ,
DOI : 10.1145/368300.368308
Safety Verification of Hybrid Systems Using Barrier Certificates, pp.477-492, 2004. ,
DOI : 10.1007/978-3-540-24743-2_32
Safety verification of hybrid systems by constraint propagation-based abstraction refinement, ACM Transactions on Embedded Computing Systems, vol.6, issue.1, 2007. ,
Some undecidable problems involving elementary functions of a real variable, The Journal of Symbolic Logic, vol.33, issue.04, pp.514-520, 1968. ,
DOI : 10.2307/1970289
Automatic invariant generation for hybrid systems using ideal fixed points, Proceedings of the 13th ACM international conference on Hybrid systems: computation and control, HSCC '10, pp.221-230, 2010. ,
DOI : 10.1145/1755952.1755984
Constructing invariants for hybrid systems, FMSD, vol.32, issue.1, pp.25-55, 2008. ,
Relational Abstractions for Continuous and Hybrid Systems, pp.686-702, 2011. ,
DOI : 10.1007/s10703-007-0044-3
Recasting nonlinear differential equations as S-systems: a canonical nonlinear form, Mathematical Biosciences, vol.87, issue.1, pp.83-115, 1987. ,
DOI : 10.1016/0025-5564(87)90035-6
Algebraic and geometric aspects of the theory of polynomial vector fields Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series, vol.408, pp.429-467, 1993. ,
Algebraic particular integrals, integrability and the problem of the center, Transactions of the American Mathematical Society, vol.338, issue.2, pp.799-841, 1993. ,
DOI : 10.1090/S0002-9947-1993-1106193-6
Nonlinear Dynamics and Chaos, 1994. ,
Comparing timed and hybrid automata as approximations of continuous systems, Hybrid Systems IV, pp.361-377, 1996. ,
DOI : 10.1007/BFb0031569
A Decision Method for Elementary Algebra and Geometry, Bulletin of the American Mathematical Society, vol.59, 1951. ,
DOI : 10.1007/978-3-7091-9459-1_3
Series of Abstractions for Hybrid Automata, LNCS, vol.2289, pp.465-478, 2002. ,
DOI : 10.1007/3-540-45873-5_36
Abstractions for hybrid systems, Formal Methods in System Design, vol.92, issue.3, pp.57-83, 2008. ,
DOI : 10.1007/s10703-007-0044-3
Generating Box Invariants, LNCS, vol.4981, pp.658-661, 2008. ,
DOI : 10.1007/978-3-540-78929-1_58
Nonlinear Systems: Approximating Reach Sets, pp.600-614, 2004. ,
DOI : 10.1007/978-3-540-24743-2_40
Polynomial Level-Set Method for Polynomial System Reachable Set Estimation, IEEE Transactions on Automatic Control, vol.58, issue.10, pp.2508-2521, 2013. ,
DOI : 10.1109/TAC.2013.2263916
Introduction to Applied Nonlinear Dynamical Systems and Chaos, Texts in Applied Mathematics, vol.2, 2003. ,
DOI : 10.1007/978-1-4757-4067-7
Tangent cone and contingent cone to the intersection of two closed sets. Nonlinear Analysis: Theory, Methods & Applications, vol.73, issue.5, pp.1203-1220, 2010. ,
A symbolic approach for the safety verification of continuous systems, Proceedings of the International Conference on Computational Sciences, pp.93-100, 2007. ,
Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants, pp.354-373, 2013. ,
DOI : 10.1007/978-3-642-32759-9_38