  Since the classical proportional-integral-derivative (PID) controller is the
most widely and successfully used ones in industrial processes, it is of vital
importance to investigate theoretically the rationale of this ubiquitous
controller in dealing with nonlinearity and uncertainty. Recently, we have
investigated the capability of the classical PID control for second order
nonlinear uncertain systems and provided some analytic design methods for the
choices of PID parameters, where the system is assumed to be in the canonical
form of cascade integrators. In this paper, we will consider the natural
extension of the classical PID control for high order affine-nonlinear
uncertain systems. In contrast to most of the literature on controller design
of nonlinear systems, we do not require such special system structures as
pure-feedback form, thanks to the strong robustness of the extend PID
controller. To be specific, we will show that under some suitable conditions on
nonlinearity and uncertainty of the systems, the extended PID controller can
globally(or semi-globally) stabilize the nonlinear uncertain systems, and at
the same time the regulation error converges to $0$ exponentially fast, as long
as the control parameters are chosen from an open unbounded parameter manifold.
