Output regulation of some classes of SISO non-minimum phase non-affine systems

The paper addresses the output tracking problem for a class of non-affine nonlinear systems with unstable zero-dynamics. The chosen output has to track a signal which is the sum of a known number of sinusoids with known frequency (amplitude and phase are instead unknown). Due to the non-minimum phase nature of the considered systems, the direct tracking by standard sliding mode methods generates unstable behaviors of the internal dynamics. The proposed method relies on the properties of differentially flat systems under mild assumptions relevant to the relation between the original output and a suitably designed flat output. As a result the original problem is transformed in a state-tracking problem of invertible stable systems, where any internal state turns out to be bounded.