Technical Report On the Nonlinear Stabilization Problem via Quadratic Immersion Part I: Sigma/Pi-systems and biased solutions of driver-type systems.

Carravetta, Francesco

Based on our recently issued paper on Quadratic Immersion (QI), (also said 'exact quadratization') for nonlinear control systems, the present work aims to define the main features of a possible new approach in nonlinear control, able to exploit the structural properties of a quadratized system in order to design global, statefeedback-regulators, with an exponential, and tunable, performance, for a meaningful class of nonlinear systems. The paper is divided into two parts. In the Part I we go through theproperties of QI and explore the possibility of writing explicitly the solution for the class of the, so called, Sigma/Pi-systems. The main result consists in showing that, under certain conditions, Sigma/Pi-systems are always forward complete, and the solution can be calculated at the steady-state.

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