Semi-global stabilization of minimum phase nonlinear systems in special normal forms

Abstract

We semi-globally stabilize certain minimum phase nonlinear systems which are in a normal form where the nonlinear subsystem is driven by an output of a linear system that possesses (possibly) nonzero peaking exponents. We eliminate the peaking phenomenon by stabilizing part of the linear system with a high-gain linear control and part of the linear system with a small, bounded control. The interpretation of this approach will be that we are redefining the outputs to add asymptotically stable nonlinear zeros to the system in a manner that allows the new composite zero dynamics to be asymptotically stable on arbitrarily large compact sets.