Hybrid output regulation for linear systems with periodic jumps: solvability conditions, structural implications and semi-classical solutions

The problem of output regulation for a class of hybrid linear systems characterized by periodic jumps is considered in this paper. Necessary and sufficient conditions for its solution are provided both in the full information and error feedback case. By a detailed analysis of such conditions, several interesting properties are derived, including the fact that the regulator must contain a (suitably defined) copy of the flow zero dynamics of the plant in addition to the usual copy of the exosystem dynamics, and the fact that the output regulation problem is generically solvable for fat plants (having more inputs than outputs) and generically not solvable for square plants. In addition, semi-classical solutions to the hybrid output regulation problem are introduced and discussed. Such solutions are characterized by the property that the required steady-state input can be generated as a simple linear function of the state of the exosystem (as in the non-hybrid case), although the associated steady-state response has a genuinely hybrid structure.