Global asymptotic stabilization of systems 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 on whether the state is near or far from the origin. The proposed approach is based on uniting control Lyapunov functions. In this framework, the stabilization problem may be recast as an LMI optimization problem for which powerful semidefinite programming softwares exist. This is illustrated by means of three numerical examples.