A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations

Abstract

We establish the local input-to-state stability of a large class of disturbed nonlinear reaction–diffusion equations w.r.t. the global attractor of the respective undisturbed system.

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Acknowledgements

S. Dashkovskiy and O. Kapustyan are partially supported by the German Research Foundation (DFG) and the State Fund for Fundamental Research of Ukraine (SFFRU) through the joint German-Ukrainian grant “Stability and robustness of attractors of nonlinear infinite-dimensional systems with respect to disturbances” (DA 767/12-1).

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Correspondence to Jochen Schmid.

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Published in the topical collection Input-to-state stability for infinite-dimensional systems.

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Dashkovskiy, S., Kapustyan, O. & Schmid, J. A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations. Math. Control Signals Syst. 32, 309–326 (2020). https://doi.org/10.1007/s00498-020-00256-w

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Keywords

  • Local input-to-state stability
  • Global attractor
  • Nonlinear reaction–diffusion equations