Abstract.
An important approach to decidability questions for verification algorithms of hybrid systems has been the construction of a bisimulation. Bisimulations are finite state quotients whose reachability properties are equivalent to those of the original infinite state hybrid system. In this paper we introduce the notion of o-minimal hybrid systems, which are initialized hybrid systems whose relevant sets and flows are definable in an o-minimal theory. We prove that o-minimal hybrid systems always admit finite bisimulations. We then present specific examples of hybrid systems with complex continuous dynamics for which finite bisimulations exist.
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Date received: June 9, 1998. Date revised: June 28, 1999.
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Lafferriere, G., Pappas, G. & Sastry, S. O-Minimal Hybrid Systems. Math. Control Signals Systems 13, 1–21 (2000). https://doi.org/10.1007/PL00009858
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DOI: https://doi.org/10.1007/PL00009858