Output Regulation by Error Dynamic Feedback in Linear Time-Invariant Hybrid Dynamical Systems

This work deals with the problem of output regulation in multivariable linear time-invariant hybrid dynamical systems. Namely, the problem of finding a feedback regulator achieving asymptotic tracking of a reference signal generated by an exogenous system and global asymptotic stability of the closed-loop dynamics is tackled for a class of hybrid systems featuring a continuous-time linear dynamics subject to state jumps triggered by a time-driven measurable signal. Necessary and sufficient conditions for the existence of a solution are derived on the basis of the geometric properties of the given hybrid exosystem and plant. The if-part of the proof shows how to synthesize the feedback hybrid regulator on those conditions. A numerical example is worked out with the aim of illustrating how to apply the devised approach.