State feedback control of nonlinear quadratic systems

This work deals with the problem of stabilizing a generic nonlinear quadratic system via state feedback control. More precisely, given a polytopic region surrounding the origin of the state space, the design procedure is aimed at finding a static state feedback controller such that the zero equilibrium point of the closed loop system is asymptotically stable and the given polytope belongs to the domain of attraction of such equilibrium point. Furthermore, it is shown that the proposed results yield a linear matrix inequalities (LMIs) feasibility problem, which can be efficiently tackled, as illustrated by means of a numerical example.