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

Stability Analysis of Fractional Order Systems Described in the Lur'e Structure