Computing output feedback controllers to enlarge the domain of attraction in polynomial systems

The problem of computing controllers to enlarge the domain of attraction (DA) of equilibrium points of polynomial systems is considered. In order to deal with such a problem, a technique for computing static nonlinear output feedback controllers, which maximize the largest estimate of the DA (LEDA) induced by a given polynomial Lyapunov function, is proposed. The main contribution of the note is to show that a lower bound of the maximum achievable LEDA and a corresponding controller can be obtained through linear matrix inequality optimizations. Moreover, a necessary condition for tightness of this lower bound is presented, which is also a sufficient condition to establish the tightness of the lower bound of the LEDA for a given controller.