WIAS Preprint No. 687, (2001)

Longtime dynamics in adaptive gain control systems


  • Leonov, Gennady A.
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 93C40 34D23 34D05 34D45 93C80


  • adaptive control systems, frequency domain methods, global attractor, Hausdorff dimension




We study the longtime dynamics of a nonlinear adaptive control system introduced by Mareels et al. [10] to control the behavior of a plant which can be described by a finite dimensional SISO linear time invariant system stabilizable by a high gain output feedback. We apply frequency domain methods to derive conditions for global stability, to approximate the region containing the global attractor and to estimate its Hausdorff dimension.

Appeared in

  • Lecture Notes in Control and Inform. Sci., 273 (2002), pp. 241-254

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