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Abstract The problems of robustness with respect to external inputs and of convergence rate estimation are considered for the so‐called sub‐optimal nonlinear damping control. To this end, existence of solutions is justified, a strict Lyapunov function is found and its properties are investigated. The hyperexponential convergence of the unperturbed sub‐optimal nonlinear damping control is demonstrated. Moreover, an integral extension is proposed to complement the controller with capability of compensation for static errors. The results are illustrated by numeric simulations and the control experiments.
Efimov et al. (Sun,) studied this question.