Semi-Global Stabilization of Partially Linear Composite Systems via Linear High-and-Low-Gain State Feedback

This paper extends the recent results of [8] on semi-global stabilisation 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 [8]. More specifically, we show, by explicit construction of the control laws, that a cascade of linear stabilisable and nonlinear asymptotically stable subsystems is semi-globally stabilisable by a linear dynamic feedback of the state of the linear subsystem if the linear subsystem is right invertible and has all its invariant seros in the closed left half s-plane. Our 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.