Zeros and poles of transfer functions 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. It is shown firstly that knowledge of the transfer function permits the computation in closed-form of the complete forced (state or output) response of the hybrid plant. Moreover, hybrid transfer functions resulting from standard interconnection schemes - such as parallel, series and feedback interconnection - are derived. The intrinsically related notions of zero and pole of such transfer function are then discussed in details. Finally, the crucial role played by zeros of a transfer function in the output zeroing is emphasized and extended to the hybrid context.