  In this article we study algorithmic synthesis of the class of stabilizing
switching signals for discrete-time switched linear systems proposed in [12]. A
weighted digraph is associated in a natural way to a switched system, and the
switching signal is expressed as an infinite walk on this weighted digraph. We
employ graph-theoretic tools and discuss different algorithms for designing
walks whose corresponding switching signals satisfy the stabilizing switching
conditions proposed in [12]. We also address the issue of how likely/generic it
is for a family of systems to admit stabilizing switching signals, and under
mild assumptions give sufficient conditions for the same. Our solutions have
both deterministic and probabilistic flavours.
