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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 2, 2000, pp. 469–487
DOI: 10.4171/ZAA/962

Published online: 2000-06-30

Asymptotically Stable Almost-Periodic Oscillations in Systems with Hysteresis Nonlinearities

M. Brokate[1], I. Collings[2], A.V. Pokrovskii[3] and F. Stagnitti[4]

(1) Technische Universität München, München Garching, Germany
(2) Deakin University, Geelong, Australia
(3) Russian Academy of Sciences, Moscow, Russian Federation
(4) Deakin University, Warnambool, Australia

We present some sufficient conditions for the asymptotic stability of forced almostperiodic oscillations in nonlinear systems subject to small hysteresis perturbations. The main technical restriction on hysteresis nonlinearity comes to a contraction-type property, which holds for some classical models of hysteresis. Also we require a special stability property of the unperturbed system in the sense of Lyapunov and the bounded input-bounded output.

Keywords: Nonlinear dynamical systems, almost periodic oscillations, hysteresis nonlinearities, asymptotic stability

Brokate M., Collings I., Pokrovskii A.V., Stagnitti F.: Asymptotically Stable Almost-Periodic Oscillations in Systems with Hysteresis Nonlinearities. Z. Anal. Anwend. 19 (2000), 469-487. doi: 10.4171/ZAA/962