About the positivity of a class of hybrid dynamic linear systems

This paper deals with the characterization of the main properties of positivity, excitability, output excitability and transparency of a class of single-input single-output hybrid systems which consist of two coupled continuous-time and digital subsystems. Precise sufficient conditions as well as necessary and sufficient conditions that guarantee the existence of such properties are formulated. It is found that, on occasions and depending on particular parameterizations, the couplings between the digital and continuous-time dynamics make possible the achievement or not of such properties. An extended discrete system whose state vector is composed of the digital one and of the discretization of the continuous one at sampling instants is used as a key element in the analysis since excitability of such a system implies that of the whole hybrid one while the contrary is not true in general.