Output regulation of hybrid linear systems: solvability conditions and structural implications

Abstract

Hybrid output regulation aims at ensuring that the output of a hybrid system under control converges to a desired reference, despite the influence of unknown initial conditions and unmeasured disturbances, assuming that both references and disturbances are described as the output of an exosystem with a known model and unknown initial state. The main objective of this paper is to show how structural methods, based on tools from the geometric approach to control theory, allow a deep understanding of a plethora of surprising and unprecedented phenomena arising in output regulation problems for linear hybrid systems in the presence of time-driven periodic jumps, which do not possess any counterpart in classical output regulation.