Semi-global stabilization of partially linear composite systems via feedback of the state of the linear part

The problem of semi-global stabilization of a class of partially linear composite systems is considered. It is shown by explicit construction of the control laws, that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi-globally stabilizable by a dynamic feedback of the state of the linear subsystem if the linear subsystem is right invertible and has all its invariant zeros in the closed left half s-plane, and the only linear variables entering the nonlinear subsystem are the output of the linear subsystem