Non-resonance conditions for uniform observability in the problem of nonlinear output regulation

This paper deals with the design of an internal model-based semiglobal output feedback regulator for possibly nonminimum phase nonlinear systems. Taking advantage of the design tool proposed in Isidori (IEEE Trans. Automat. Control 45 (10) 2000), we show how the problem of output regulation can be reformulated into an output feedback stabilization problem of a suitably defined extended auxiliary system. The output feedback stabilization of the extended auxiliary system is addressed in the second part of the paper, where an observer-based stabilizer is proposed. The existence of the latter is characterized in terms of necessary and sufficient conditions which can be interpreted as nonlinear non-resonance conditions between the modes of the exosystem and the zero dynamics of the controlled plant. (C) 2004 Elsevier B.V. All rights reserved.