Interpretability of Path-Complete Techniques and Memory-based Lyapunov functions

Della Rossa, Matteo;Jungers, Raphaël
(2023) IEEE Control Systems Letters — Vol. 7, p. 781-786 (2023)

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Abstract
We study path-complete Lyapunov functions, which are stability criteria for switched systems, described by a combinatorial component (namely, an automaton), and a functional component (a set of candidate Lyapunov functions, called the template). We introduce a class of criteria based on what we call memory-based Lyapunov functions, which generalize several techniques in the literature. Our main result is an equivalence result: any path-complete Lyapunov function is equivalent to a memory-based Lyapunov function, however defined on another template. We show the usefulness of our result in terms of numerical efficiency via an academic example.
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Della Rossa, M., & Jungers, R. (2023). Interpretability of Path-Complete Techniques and Memory-based Lyapunov functions. IEEE Control Systems Letters, 7, 781-786. https://doi.org/10.1109/LCSYS.2022.3226627 (Original work published 2023)