On the Region of Asymptotic Stability of Nonlinear Quadratic Systems

This paper considers the following problem: given a nonlinear quadratic system and a certain box containing the origin of the state space, determine whether this box belongs to the Region of Asymptotic Stability of the zero equilibrium point of the system under consideration. Quadratic systems play an important role in the modelling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). For such systems it is of mandatory importance not only to determine whether the origin of the state space is locally asymptotically stable but also to ensure that the operative range is included into the convergence region of the equilibrium. The proposed algorithm requires the solution of a suitable feasibility problem involving Linear Matrix Inequalities constraints. Some examples illustrate the effectiveness of the proposed procedure.