Global stabilization of partially linear composite systems

Abstract

It is shown that a cascade system consisting of a linearly controllable system and a nonlinearly asymptotically stable system is globally stabilizable by smooth dynamic state feedback if the linear subsystem is right-invertible and weakly minimum phase and the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free, and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. The weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.<>