Steady-state, harmonic response and moments of linear systems with periodic jumps

By relying on the recently introduced notion of transfer function for linear hybrid systems with periodic jumps, herein we extend, for the first time, frequency-domain analysis tools - well-known and extensively used in the context of purely continuous or discrete time systems - to such a class of hybrid systems. In fact, knowledge of the transfer function allows for the frequency-domain definition of the notion of 0-th momentof the underlying hybrid system, which is instrumental, e.g. for the solution to model reduction or input-output 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. To further substantiate the theoretical claims, the paper is concluded by the frequency-domain robustness analysis of the classical consensus protocol in the presence of sampled measurements.