  In the present work, the averaged fidelity is introduced as the steering
parameter. According to the definitions of steering from Alice to Bob, a
general scheme for designing linear steering criteria is developed for a
high-dimensional system. For a given set of measurements on Bob's side, two
quantities, the so-called nonsteering thresholds, can be defined. If the
measured averaged fidelity exceeds these thresholds, the state shared by Alice
and Bob is steerable from Alice to Bob, and the measurements performed by Alice
are also verified to be incompatible. Within the general scheme, we also
construct a linear steering inequality when the set of measurements performed
by Bob has a continuous setting. Some applications are also provided.
