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- W4287780775 abstract "We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined hybrid complete Lyapunov function exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings." @default.
- W4287780775 created "2022-07-26" @default.
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- W4287780775 date "2020-05-06" @default.
- W4287780775 modified "2023-09-24" @default.
- W4287780775 title "Conley's fundamental theorem for a class of hybrid systems" @default.
- W4287780775 doi "https://doi.org/10.48550/arxiv.2005.03217" @default.
- W4287780775 hasPublicationYear "2020" @default.
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