Osservatori e regolazione robusta dell'uscita per sistemi non lineari

The objective of this thesis is twofold: on one hand, the design of nonliner observers, on the other, the design of internal-model regulators to solve the robust output regulation problem. In the observer theory a key role is played by the so called high-gain observers. The purpose of the first part of the thesis is to propose novel techniques which allow to overcome or at least to mitigate some of the main drawbacks characterizing this class of observers. Firstly, we study the possibility of writing an observer for multi-input multi-output observable systems in the original coordinates. Then, we propose a novel class of high-gain observers, denoted as ``low-power'', which allows to overcome numerical problems, to avoid the peaking phenomenon and to improve the sensitivity properties to high-frequency measurement noise. The second part of the thesis addresses the output regulation problem, solved for linear systems during the 70's by Francis and Wonham who coined the celebrated ``internal model principle''. Constructive solutions have also been proposed in the nonlinear framework but under restrictive assumptions that reduce the class of systems to which this methodology can be applied. In this thesis we focus on the output regulation problem in presence of periodic disturbances and we propose a novel approach which allows to consider a broader class of nonlinear systems. With the proposed design the stabilization problem and the regulation problem are substantially decoupled and output regulation is achieved in presence of uncertainties or disturbances, as long as the trajectories of the resulting closed-loop system are bounded.