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• W3022816144 abstract "We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of dynamical systems. The version of (i) asserts that a globally-defined hybrid complete Lyapunov function exists for every 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 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 systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings." @default.
• W3022816144 created "2020-05-13" @default.
• W3022816144 creator A5002498364 @default.
• W3022816144 creator A5068996884 @default.
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• W3022816144 date "2020-05-07" @default.
• W3022816144 modified "2023-09-27" @default.
• W3022816144 title "Conley's fundamental theorem for a class of hybrid systems" @default.
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• W3022816144 hasPublicationYear "2020" @default.
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