Robust control of quadratic systems with norm bounded uncertainties

This paper deals with the problem of the stabilization of uncertain quadratic systems via state feedback. The main contribution of the paper is a control design methodology which enables to find a robust controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point. This design procedure involves the solution of a Linear Matrix Inequalities (LMIs) feasibility problem, which can be efficiently solved via available optimization algorithms. A numerical example shows the effectiveness of the proposed methodology.