  This paper presents some new propositions related to the fractional order
$h$-difference operators, for the case of general quadratic forms and for the
polynomial type, which allow proving the stability of fractional order
$h$-difference systems, by means of the discrete fractional Lyapunov direct
method, using general quadratic Lyapunov functions, and polynomial Lyapunov
functions of any positive integer order, respectively. Some examples are given
to illustrate these results.
