  The dynamical behavior of switched affine systems is known to be more
intricate than that of the well-studied switched linear systems, essentially
due to the existence of distinct equilibrium points for each subsystem. First,
under arbitrary switching rules, the stability analysis must be generally
carried out with respect to a compact set with non-empty interior rather than
to a singleton. We provide a novel proof technique for existence and outer
approximation of attractive invariant sets of a switched affine system, under
the hypothesis of global uniform stability of its linearization. On the other
hand, considering dwell-time switching signals, forward invariant sets need not
exist for this class of switched systems, even for stable ones. Hence, more
general notions of stability/boundedness are introduced and studied,
highlighting the relations of these concepts to the uniform stability of the
linear part of the system under the same class of dwell-time switching signals.
These results reveal the main differences and specificities of switched affine
systems with respect to linear ones, providing a first step for the analysis of
switched systems composed by subsystems not sharing the same equilibrium.
Numerical methods based on linear matrix inequalities and sum-of-squares
programming are presented and illustrate the developed theory.
