  Given a family of systems, identifying stabilizing switching signals in terms
of infinite walks constructed by concatenating cycles on the underlying
directed graph of a switched system that satisfy certain conditions, is a
well-known technique in the literature. This paper deals with a new {method to
design} these cycles for stability of switched linear systems. We employ
properties of the subsystem matrices and mild assumption on the admissible
switches between the subsystems {for this purpose}. In contrast to prior works,
{our construction of} stabilizing cycles does not involve design of
Lyapunov-like functions and storage of sets of scalars in memory prior to the
application of a cycle detection algorithm. As a result, {the} techniques
{proposed in this paper} offer improved numerical tractability.
