This paper presents a novel observer-based method for estimating the parameters
of an exponentially damped sinusoid, including the frequency, amplitude, phase and the
damping factor. A second-order sliding-mode-based adaptation law is designed for estimating
the frequency and the damping factor, while amplitude and phase are obtainable from the said
parameters by straightforward algebra. The stability and robustness analysis in presence of an
additive disturbance proves the existence of a tuning parameter set for which the estimator’s
dynamics are asymptotic stable and the estimation error asymptotically converges to a residual
set whose size depends on the amplitude of the disturbance. Numerical and comparative
examples show the effectiveness of the proposed estimation approach.
