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Lyapunov Stability of Differential Inclusions with Lipschitz Cusco Perturbations of Maximal Monotone Operators

  • Samir Adly
  • Abderrahim HantouteEmail author
  • Bao Tran Nguyen
Article
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Abstract

We give new criteria for weak and strong invariant closed sets for differential inclusions in \(\mathbb {R}^{n}\), and which are simultaneously governed by Lipschitz Cusco mapping and by maximal monotone operators. Correspondingly, we provide different characterizations for the associated strong Lyapunov functions and pairs. The resulting conditions only depend on the data of the system, while the invariant sets are assumed to be closed, and the Lyapunov pairs are assumed to be only lower semi-continuous.

Keywords

Differential inclusions Cusco mappings Maximal monotone operators a-Lyapunov pairs Invariant sets 

Mathematics Subject Classification (2010)

37B25 47J35 93B05 

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Notes

Acknowledgements

The authors would like to thank the referees for providing valuable comments and suggesting new references, which allowed to improve the manuscript and the presentation of the results.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Samir Adly
    • 1
  • Abderrahim Hantoute
    • 2
    Email author
  • Bao Tran Nguyen
    • 3
  1. 1.XLIM UMR-CNRS 7252Université de LimogesLimogesFrance
  2. 2.Center for Mathematical Modeling (CMM)Universidad de ChileSantiagoChile
  3. 3.Universidad de O’HigginsRancaguaChile

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