Vector Barrier Certificates and Comparison Systems

International audienceVector Lyapunov functions are a multi-dimensional extension of the more familiar (scalar) Lyapunov functions, commonly usedto prove stability properties in systems of non-linear ordinary differential equations (ODEs). This paper explores an analogous vector extensionfor so-called barrier certificates used in safety verification. As with vector Lyapunov functions, the approach hinges on constructing appropriatecomparison systems, i.e., related differential equation systems from whichproperties of the original system may be inferred. The paper presents anaccessible 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 insafety verification and invariant synthesis