Abstract
The bifurcation of limit cycles in single-input single-output control systems with saturation is considered. Under some non-degeneracy conditions, a theorem characterizing such bifurcation is stated for the cases of dimension two and three. In terms of the deviation from the critical value of the bifurcation parameter, expressions in form of power series for the period, amplitude and the characteristic multipliers of the bifurcating limit cycle are obtained. These results are similar to the Hopf bifurcation theorem for differentiable systems, but they show some differences coming from the non-smooth character of the saturation characteristic.
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