@article{DashkovskiySlynko2022,
  author    = {Dashkovskiy, Sergey and Slynko, Vitalii},
  title     = {Stability conditions for impulsive dynamical systems},
  series = {Mathematics of Control, Signals, and Systems},
  volume    = {34},
  journal   = {Mathematics of Control, Signals, and Systems},
  number    = {1},
  issn      = {1435-568X},
  doi       = {10.1007/s00498-021-00305-y},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-268390},
  pages     = {95-128},
  year      = {2022},
  abstract  = {In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.},
  language  = {en}
}
@article{DashkovskiyKapustyanSchmid2020,
  author    = {Dashkovskiy, Sergey and Kapustyan, Oleksiy and Schmid, Jochen},
  title     = {A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations},
  series = {Mathematics of Control, Signals, and Systems},
  volume    = {32},
  journal   = {Mathematics of Control, Signals, and Systems},
  number    = {3},
  doi       = {10.1007/s00498-020-00256-w},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-281099},
  pages     = {309-326},
  year      = {2020},
  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.},
  language  = {en}
}