  This paper proposes several definitions of robust stability for logic
dynamical systems (LDSs) with uncertain switching, including robust/uniform
robust set stability and asymptotical (or infinitely convergent)/finite-time
set stability with ratio one. It is proved herein that an LDS is robustly set
stable if and only if the destination set contains all loops (i.e., the paths
from each state to itself); an LDS is uniformly robustly set stable, or
finite-time set stable with ratio one, if and only if all states outside the
destination set are unreachable from any self-reachable state; and an LDS is
asymptotically set stable with ratio one if and only if the largest robustly
invariant subset (LRIS) in the destination set is reachable from any state. In
addition, it is proved that uniform robust set stability implies robust set
stability, and robust set stability implies asymptotical set stability with
ratio one. However, the inverse claims are not generally true. The relations
between robust stability and stability under random switching are revealed,
that is, the asymptotical/finite-time set stability with ratio one under
uncertain switching is equivalent to asymptotical/finite-time set stability of
the LDS under random switching. Furthermore, it is proved that, for uniform set
stability and asymptotical/finite-time set stability with ratio one, the set
stability is equivalent to the stability with respect to the LRIS in the
destination set. However, robust set stability does not imply robust stability
with respect to the LRIS in the destination set. This finding corrects a result
in a previous study.
