  The notion of path-complete positivity is introduced as a way to generalize
the property of positivity from one LTI system to a family of switched LTI
systems whose switching rule is constrained by a finite automaton. The
generalization builds upon the analogy between stability and positivity, the
former referring to the contraction of a norm, the latter referring to the
contraction of a cone (or, equivalently, a projective norm). We motivate and
investigate the potential of path-positivity and we propose an algorithm for
the automatic verification of positivity.
