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

Abstract

This paper extends the results of the authors (1992) on semi-global stabilization of a class of minimum-phase nonlinear systems via linear state feedback. The class of minimum-phase nonlinear systems considered in this paper subsume those of the previous paper. More specifically, the authors show, by explicit construction of the control laws, that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi-globally stabilizable by linear 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. The authors' proposed linear dynamic state feedback control law has a single tunable gain parameter that allows for local asymptotical stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set. >