  Self-excited systems arise in many applications, such as biochemical systems,
mechanical systems with fluid-structure interaction, and fuel-driven systems
with combustion dynamics. This paper presents a Lur'e model that exhibits
biased self-excited oscillations under constant inputs. The model involves
asymptotically stable linear dynamics, time delay, a washout filter, and a
saturation nonlinearity. For all sufficiently large scalings of the loop
transfer function, these components cause divergence under small signal levels
and decay under large signal amplitudes, thus producing an oscillatory
response. A bias-generation mechanism is used to specify the mean of the
oscillation. The main contribution of the paper is a detailed analysis of a
discrete-time version of this model.
