Nonlinear analysis for verifying closed-loop stability before inserting a new controller

Suppose a nonlinear plant is stabilized by a nonlinear controller, and further assume that the plant is unknown but the controller is known. Suppose also that the use of a new controller appears attractive. This paper extends our results for linear time-invariant systems and proposes novel nonlinear analysis results, utilizing the kernel representation of nonlinear systems, for ensuring that the introduction of the new nonlinear controller will stabilize the plant.