  The paper presents a model reduction framework geared towards the analysis
and design of systems that switch and oscillate. While such phenomena are
ubiquitous in nature and engineering, model reduction methods are not well
developed for non-equilibrium behaviors. The proposed framework addresses this
need by exploiting recent advances on dominance theory. Classical balanced
truncation for linear time-invariant systems is used to develop a
dominance-preserving model reduction method for Lure systems, i.e. systems that
can be decomposed as the feedback interconnection of a linear system and a
static nonlinearity. The method is illustrated by approximating the oscillatory
behavior of a discretized heat flow control system.
