  We study computational questions related with the stability of discrete-time
linear switching systems with switching sequences constrained by an automaton.
We first present a decidable sufficient condition for their boundedness when
the maximal exponential growth rate equals one. The condition generalizes the
notion of the irreducibility of a matrix set, which is a well known sufficient
condition for boundedness in the arbitrary switching (i.e. unconstrained) case.
Second, we provide a polynomial time algorithm for deciding the dead-beat
stability of a system, i.e. that all trajectories vanish to the origin in
finite time. The algorithm generalizes one proposed by Gurvits for arbitrary
switching systems, and is illustrated with a real-world case study.
