Results on non-linear hybrid output regulation

We take preliminary steps in the field of hybrid output regulation for nonlinear systems by presenting necessary and sufficient conditions for the design of hybrid regulators. Necessary conditions are formulated in a quite general setting of “pre-asymptotic” output regulation in which closed-loop hybrid trajectories are not necessarily complete. The key notion of the hybrid internal model property is characterized in the considered hybrid setting. In the second part of the paper, more constructive sufficient conditions for the design of the regulator are given by restricting the attention to hybrid systems whose flow and jump conditions are governed by an exogenous clock-variable that implements an average dwell-time constraint.