Characterization of the ordering of path-complete stability certificates with addition-closed templates
(2023) 26th ACM International Conference on Hybrid Systems: Computation and Control — Location: San Antonio, TX, USA (9.May.2023)
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- Authors
Debauche, Virginie 
- Abstract
- As part of the development of Lyapunov techniques for cyberphysical systems, we study and compare graph-based stability certificates with respect to their conservatism. Previous work have highlighted the dependence of this ordering with respect to the properties of the chosen template of candidate Lyapunov functions. We extend here previous results from the literature to the case of templates closed under addition, as for instance the set of quadratic functions. In this context, we provide a characterization of the ordering, using an approach based on abstract operations on graphs, called lifts, which encode in a combinatorial way the algebraic properties of the chosen template. We finally provide a numerical method to algorithmically check the ordering relation.
- Affiliations
Citations
Debauche, V., Della Rossa, M., & Jungers, R. (2023). Characterization of the ordering of path-complete stability certificates with addition-closed templates. 26th ACM International Conference on Hybrid Systems: Computation and Control, San Antonio, TX, USA. https://hdl.handle.net/2078.5/252382