Non-coercive Lyapunov functions for infinite-dimensional systems |
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Authors: | Andrii Mironchenko Fabian Wirth |
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Affiliation: | Faculty of Computer Science and Mathematics, University of Passau, Innstraße 33, 94032 Passau, Germany |
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Abstract: | We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied. For evolution equations in Banach spaces with Lipschitz continuous nonlinearities these additional assumptions become especially simple. The results encompass some recent results on linear switched systems on Banach spaces. Finally, we derive new non-coercive converse Lyapunov theorems and give some examples showing the necessity of our assumptions. |
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Keywords: | Nonlinear control systems Infinite-dimensional systems Lyapunov methods Global asymptotic stability |
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