  Lur'e systems are feedback interconnection of a linear time-invariant
subsystem in the forward path and a memoryless nonlinear one in the feedback
path, which have many physical representatives. In this paper, some classical
theorems about the L2 input-output stability of integer order Lur'e systems are
discussed, and the conditions under which these theorems can be applied in
fractional order Lur'e systems with an order between 0 and 1 are investigated.
Then, application of circle criterion is compared between Lur'e systems of
integer and fractional order using their corresponding Nyquist plots.
Furthermore, applying Zames-Falb and generalized Zames-Falb theorems, some
classes of stable fractional order Lur'e systems are introduced. Finally, in
order to generalize the off-axis circle criterion to fractional order systems,
another method is presented to prove one of the theorems used in its overall
proof.
