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Vector Barrier Certificates and Comparison Systems

Abstract : Vector Lyapunov functions are a multi-dimensional extension of the more familiar (scalar) Lyapunov functions, commonly used to prove stability properties in systems of non-linear ordinary differential equations (ODEs). This paper explores an analogous vector extension for so-called barrier certificates used in safety verification. As with vector Lyapunov functions, the approach hinges on constructing appropriate comparison systems, i.e., related differential equation systems from which properties of the original system may be inferred. The paper presents an accessible development of the approach, demonstrates that most previous notions of barrier certificate are special cases of comparison systems, and discusses the potential applications of vector barrier certificates in safety verification and invariant synthesis.
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Contributor : Khalil Ghorbal <>
Submitted on : Friday, January 4, 2019 - 3:09:28 PM
Last modification on : Tuesday, February 25, 2020 - 8:08:11 AM

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Andrew Sogokon, Khalil Ghorbal, Yong Kiam Tan, André Platzer. Vector Barrier Certificates and Comparison Systems. FM 2018 - 22nd International Symposium on Formal Methods, Jul 2018, Oxford, United Kingdom. pp.418-437, ⟨10.1007/978-3-319-95582-7_25⟩. ⟨hal-01969800⟩



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