Steady-state, harmonic response and moments of linear systems with periodic jumps. (January 2021) - Galeani, Sergio; Possieri, Corrado; Sassano, Mario
Abstract: 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 moment of 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.