The paper investigates the exponential stability criterion for an
axially moving string system driven by a nonlinear partial differential
equation with nonlinear boundary feedback.The control criterion based on
a sector condition contains a large class of nonlinearities, which is a
negative feedback of the velocity at the right boundary of the moving
string. By invoking nonlinear semigroup theory, the well-posedness
result of the closed-loop system is verified under the sector criteria.
Furthermore, a novel energy like function is constructed to establish
the exponential stability of the closed-loop system by using a
integral-type multiplier method and the generalized Gronwall-type
integral inequality.