Essential and redundant internal models in nonlinear output regulation

This paper is focused on the problem of output regulation for nonlinear systems within the main framework developed in cite{SICON06}. The main goal is to complement the theory presented in cite{SICON06} with some new results showing how the dimension of the internal model-based regulator can be reduced by preserving the so-called internal model property. It is shown how the problem of reducing the regulator dimension can be approached by identifying ``observability" parts of the so-called steady-state input generator system. A local analysis based on canonical geometric tools and local observability decomposition is also presented to identify lower bounds on the regulator dimension. Possible benefits in designing redundant internal models are also presented.