Concatenability of behaviors in hybrid system interconnection

The paper is concerned with a behavioral approach to analysis of hybrid system interconnections. The hybrid system interconnection is defined as a dynamical system consisting of past and future trajectories which are switched at a certain instant by an external switching mechanism. We define the concatenability of the behaviors of the past and future interconnections, and derive a necessary and sufficient condition for the behavioral concatenability based on the notion of a state map. If the past interconnection behavior is concatenable with the future one, every past trajectory can be continued by some future trajectory without causing any impulsive phenomena. Moreover, we show that the regular feedback structure of the future interconnection guarantees the concatenability for any past interconnections