Backstepping Designs in the Presence of Non-constant Delays on the Virtual Input

  • Nikolaos Bekiaris-Liberis
  • Mrdjan Jankovic
  • Miroslav Krstic
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 4)


We present results on stabilization of nonlinear systems in the strict-feedback form with delays affecting the virtual inputs. We consider systems with constant and time-varying delays, as well as systems with delays that depend on the current or past states, which arise in numerous applications, such as, for example, in cooling systems. The design methodology is based on the concepts of infinite-dimensional backstepping and nonlinear predictor feedback. Several illustrative examples are provided.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Nikolaos Bekiaris-Liberis
    • 1
  • Mrdjan Jankovic
    • 2
  • Miroslav Krstic
    • 3
  1. 1.University of California, BerkeleyBerkeleyUSA
  2. 2.Ford Motor CompanyDearbornUSA
  3. 3.University of California, San DiegoLa JollaUSA

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