Robust Hybrid Output Regulation for Linear Systems With Periodic Jumps: Semiclassical Internal Model Design

A complete procedure for the design of a robust output feedback regulator is proposed for a class of uncertain linear hybrid systems with periodic jumps, using a hybrid extension of the classical internal model principle. Simple conditions, testable on the plant nominal data, for the problem solvability are given. The plant is not restricted to be minimum phase, square, or single input single output. The proposed regulator has a key feature of containing an internal model composed by two main units, a flow internal model, in charge of providing the correct input to achieve regulation during flows, and a jump internal model, in charge of suitably resetting the state of the regulator at each period. The proposed procedure is illustrated by its application to a physically motivated example, for which the output regulation problem is not solvable by methods appeared thus far in the literature.