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Weak input-to-state stability: characterizations and counterexamples

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Abstract

We establish characterizations of weak input-to-state stability for abstract dynamical systems with inputs, which are similar to characterizations of uniform and of strong input-to-state stability established in a recent paper by A. Mironchenko and F. Wirth. We also investigate the relation of weak input-to-state stability to other common stability concepts, thus contributing to a better theoretical understanding of input-to-state stability theory.

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Acknowledgements

I would like to thank the German Research Foundation (DFG) financial support through the grant “Input-to-state stability and stabilization of distributed-parameter systems” (DA 767/7-1).

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Authors and Affiliations

  1. Institute for Mathematics, University of Würzburg, 97074, Würzburg, Germany

    Jochen Schmid

  2. Fraunhofer Institute for Industrial Mathematics (ITWM), 67663, Kaiserslautern, Germany

    Jochen Schmid

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  1. Jochen Schmid
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Schmid, J. Weak input-to-state stability: characterizations and counterexamples. Math. Control Signals Syst. 31, 433–454 (2019). https://doi.org/10.1007/s00498-019-00248-5

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