In this note we deal with a new observer for nonlinear systems of dimension n in canonical observability form. We follow the standard high-gain paradigm, but instead of having an observer of dimension n with a gain that grows up to power n, we design an observer of dimension 2n − 2 with a gain that grows up only to power 2.

International audienceWe address a particular problem of output regulation for multi-input multi-output nonlinear systems. Specifically, we are interested in making the stability of an equilibrium point and the regulation to zero of an output ro- bust to (small) unmodelled discrepancies between design model and actual system in particular those introducing an offset. We propose a novel procedure which is intended to be relevant to realistic scenarios, as illustrated by a (non academic) example

No abstract

In this work we present a new approach to the problem of output regulation for nonlinear systems in presence of periodic disturbances, possibly with an infinite number of harmonics. We show that, by adding a linear internal model, approximate regulation is achieved if the disturbance is small enough. Nominally all the harmonic included in the internal model are absent in the periodic steady state regulation error. Furthermore we show that the regulation error can be made arbitrarily small (in the L2 sense) by enlarging the dimension of the internal model. The novel approach relies on forwarding technique. An example is provided to show the efficacy of the result.