Nonlinear Output Regulation by Post-Processing Internal Model for Multi-Input Multi-Output Systems

The paper deals with the problem of output regulation for the class of multiinput multi-output square nonlinear systems satisfying a minimum-phase assumption and a “positivity” condition on the high-frequency gain matrix. By following a design paradigm proposed in [12] for single-input single-output nonlinear systems, it is shown how an internal model-based controller can be obtained, whose dimension depends on the number of regulated outputs and on the dimension of the exosystem. Thanks to a scalability property of the regulator structure highlighted in [10], it is shown how a “pre-processing” internal model can be shifted from input to output, yielding in this way a “post-processing” internal model. This makes it possible to run a high-gain asymptotic analysis that bypasses the need of finding a normal form, as it would normally be the case.