Output regulation by error dynamic feedback in linear time-invariant hybrid dynamical systems

This work deals with output regulation for a class of multivariable hybrid dynamical systems: namely, those characterized by a continuous-time linear time-invariant dynamics, subject to periodic state jumps. More specifically, given a hybrid plant and a hybrid exogenous system generating a reference signal, the problem consists in finding a feedback hybrid regulator that achieves asymptotic tracking of the reference signal and global asymptotic stability of the closed-loop dynamics. Necessary and sufficient conditions for the existence of a solution are derived, on the basis of the geometric properties of the given plant and of the exogenous system. The if-part of the proof shows how to synthesize the feedback regulator under those conditions. A numerical example is worked out with the aim of illustrating how to apply the devised methodology.