On the notion of transfer function for linear hybrid systems with periodic jumps

In this paper, we introduce the notion of transfer function for linear hybrid systems in the presence of time-driven periodic jumps. Such concept is employed to extend frequency-domain analysis tools - well-known and extensively used in the context of purely continuous or discrete time systems - to a class of hybrid systems. In particular, knowledge of the transfer function permits firstly the computation in closed-form of the complete forced (state or output) response of the hybrid plant. Moreover, the hybrid transfer function allows for the frequency-domain definition of the notion of 0-th moment of the underlying system, which is instrumental, e.g. for the solution to model reduction or system identification problems. It is shown, in addition, that the notion of moment based on the hybrid transfer function possesses an interesting time-domain counterpart, hence extending the results obtained for purely continuous-time systems. The paper is concluded by numerical simulations to further substantiate the theoretical claims.