Weak input-to-state stability: characterizations and counterexamples

  • Jochen SchmidEmail author
Original Article


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.


Input-to-state stability (weak, strong, uniform) Robust stability Infinite-dimensional dynamical systems with inputs 



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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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for MathematicsUniversity of WürzburgWürzburgGermany
  2. 2.Fraunhofer Institute for Industrial Mathematics (ITWM)KaiserslauternGermany

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