  We propose a new controllability property for linear time varying control
systems in finite dimension: the nonuniform complete controllability, which is
halfway between the classical Kalman's properties of complete controllability
and uniform complete controllability. This new concept is described in terms of
two gramian inequalities, which have a strong relation; as we prove in our
first result; with the property of nonuniform bounded growth for the
corresponding plant, also called uncontrolled part. On the other hand, the
second result proves that if a control system is nonuniformly completely
controllable and its plant has the property of nonuniform bounded growth, then
there exist a linear feedback control leading to a nonuniformly exponentially
stable closed--loop system.
