Leonov, Gennady A.; Schneider, Klaus R. Longtime dynamics in adaptive gain control systems. (English) Zbl 1102.93311 Colonius, Fritz (ed.) et al., Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Berlin: Springer (ISBN 3-540-42890-9). Lect. Notes Control Inf. Sci. 273, 241-254 (2002). Summary: We study the longtime dynamics of a nonlinear adaptive control system introduced by Mareels et al. 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.For the entire collection see [Zbl 0994.00036]. Cited in 1 Review MSC: 93C40 Adaptive control/observation systems 93D20 Asymptotic stability in control theory PDFBibTeX XMLCite \textit{G. A. Leonov} and \textit{K. R. Schneider}, Lect. Notes Control Inf. Sci. 273, 241--254 (2002; Zbl 1102.93311)