  This paper introduces and studies the notion of output-input stability, which
represents a variant of the minimum-phase property for general smooth nonlinear
control systems. The definition of output-input stability does not rely on a
particular choice of coordinates in which the system takes a normal form or on
the computation of zero dynamics. In the spirit of the ``input-to-state
stability'' philosophy, it requires the state and the input of the system to be
bounded by a suitable function of the output and derivatives of the output,
modulo a decaying term depending on initial conditions. The class of
output-input stable systems thus defined includes all affine systems in global
normal form whose internal dynamics are input-to-state stable and also all
left-invertible linear systems whose transmission zeros have negative real
parts. As an application, we explain how the new concept enables one to develop
a natural extension to nonlinear systems of a basic result from linear adaptive
control.
