Memory-Based Lyapunov Functions and Path-complete Framework: Equivalence and Properties
(2022) 10th International Conference on Systems and Control (ICSC) — Location: Marseille, France (23.November.2022)
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- Abstract
- In this paper, in the framework of stability analysis of switched systems, we review and analyze multiple Lyapunov functions structures. We formalize and study a class of Lyapunov functions that do not only depend on the state, but also on the past switching sequence, the ``memory'', in a general language-theory setting. We recall and extend an equivalence result between these stability criteria and a class of combinatorial Lyapunov techniques, also known as path-complete Lyapunov functions. We provide the dual results based on the knowledge/prediction of the future values of the switching signals and we illustrate our techniques via numerical examples.
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Citations
Della Rossa, M., & Jungers, R. (2022). Memory-Based Lyapunov Functions and Path-complete Framework: Equivalence and Properties. 10th International Conference on Systems and Control (ICSC), Marseille, France. https://hdl.handle.net/2078.5/164609