Synthesis of a global asymptotic stabilizing feedback law for a system satisfying two different sector conditions

Global asymptotic stabilization for a class of nonlinear systems is addressed. The dynamics of these systems are composed of a linear part to which is added some nonlinearities which satisfy two different sector bound conditions depending wether the state is closed or distant from the origin. The approach described here is based on the uniting of control Lyapunov functions as introduced in. The stabilization problem may be recast as an LMI optimization problem for which powerful semidefinite programming softwares exist. This is illustrated by a numerical example.