A note on the excitability properties of discrete-time positive switched systems

In this paper, excitability properties of discrete-time positive switched systems are introduced and investigated. When moving from positive systems to positive switched systems, two possible extensions of excitability arise, leading to the concepts of strong and weak excitability. A family of algebraic characterizations for each property is first provided. Moreover, by exploiting their “structural nature”, strong and weak excitability are characterized in graph-theoretic terms. An algorithm is described, which allows to check whether the system is strongly excitable or not. Some examples illustrate the algorithm.