Global feedback stabilization of nonlinear systems

In this paper we continue our development of the analogues for nonlinear systems of those frequency domain notions so important in classical control. One of our long-term goals, about which we can now say quite a bit in a reasonably broad framework (see 4), is to develop a design philosophy for the construction of (globally) stabilizing compensators for nonlinear systems, based on seemingly familiar notions such as the (strong) relative degree of a nonlinear system or knowledge that the system is "minimum phase." Aside from the development of a basic, "frequency domain package" for nonlinear systems, this paper contains applications to system invertibility, (global) stabilization by dynamic compensation, and global linearization by state feedback for nonlinear systems with relative degree or minimum phase properties.