Robust output regulation of linear passive systems using maximally monotone controls

The output regulation problem is addressed. We start with a linear passive system without feed-forward term and we look for a static set-valued output feedback control law which guarantees the regulation of the output to a desired fixed value, even in the presence of external matched and bounded perturbations. The multivalued control is taken as the subdifferential of some proper, convex, lower semicontinuous function with effective domain restricted to a closed convex set S, yielding to a maximally monotone set-valued map. The existence and convergence of system trajectories to an equilibrium set are established. By using the so-called Yosida approximation, some implementation issues regarding the multivalued control law are addressed. Finally, some examples are presented to illustrate the robustness features in the output of the closed-loop.