A frequency domain philosophy for nonlinear systems, with applications to stabilization and to adaptive control

In this paper we develop, in the nonlinear setting, certain of the basic elements of the frequency domain approach to linear system theory. Thus, we develop analogues of the notion of left and right half plane zeros for systems of relative degree one. It is shown that high gain output feedback stabilizes minimum phase systems of (strong) relative degree one and that lag-lead compensators can also be used to "shape the response" of nonlinear systems. We conclude with a discussion of the performance of high gain adaptive stabilizers for such nonlinear systems.