  Electrochemical impedance spectroscopy (EIS) is a widely used experimental
technique for characterising materials and electrode reactions by observing
their frequency-dependent impedance. Classical EIS measurements require the
electrochemical process to behave as a linear time-invariant system. However,
electrochemical processes do not naturally satisfy this assumption: the
relation between voltage and current is inherently nonlinear and evolves over
time. Examples include the corrosion of metal substrates and the cycling of
Li-ion batteries. As such, classical EIS only offers models linearised at
specific operating points. During the last decade, solutions were developed for
estimating nonlinear and time-varying impedances, contributing to more general
models. In this paper, we review the concept of impedance beyond linearity and
stationarity, and detail different methods to estimate this from measured
current and voltage data, with emphasis on frequency domain approaches using
multisine excitation. In addition to a mathematical discussion, we measure and
provide examples demonstrating impedance estimation for a Li-ion battery,
beyond linearity and stationarity, both while resting and while charging.

Systems and Control;Systems and Control