Journal
Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3501710.3519539
Keywords
Switched systems; path-complete Lyapunov methods; stability analysis; lifts
Funding
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [864017 - L2C]
- Innoviris Foundation
- FNRS (Chist-Era Druid-net)
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In this study, we examine the comparison of stability certificates based on path-complete Lyapunov methods in the context of discrete-time switched systems. We provide a characterization for templates that are closed under pointwise minimum/maximum, which covers several templates commonly used in practice. We use an approach based on abstract operations on graphs, called lifts, to demonstrate the dependence of the ordering on the analytical properties of the template. Additionally, we present preliminary results on another family of templates that are closed under addition, such as the set of quadratic functions.
In the context of discrete-time switched systems, we study the comparison of stability certificates based on path-complete Lyapunov methods. A characterization of this general ordering has been provided recently, but we show here that this characterization is too strong when a particular template is considered, as it is the case in practice. In the present work we provide a characterization for templates that are closed under pointwise minimum/maximum, which covers several templates that are often used in practice. We use an approach based on abstract operations on graphs, called lifts, to highlight the dependence of the ordering with respect to the analytical properties of the template. We finally provide more preliminary results on another family of templates: those that are closed under addition, as for instance the set of quadratic functions.
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