分数阶Lur'e结构系统的稳定性分析
Stability Analysis of Fractional Order Systems Described in the Lur'e Structure
摘要：
Lur'e系统是前向路径上的线性定常子系统和反馈路径上的无记忆非线性子系统的反馈互连，具有许多物理代表。本文讨论了整数阶Lur 'e系统的L2输入输出稳定性的一些经典定理，并研究了这些定理适用于0~1阶分数阶Lur' e系统的条件。然后，利用相应的Nyquist图比较了圆判据在整数阶和分数阶Lur 'e系统中的应用。进一步，应用Zames-Falb定理和推广的Zames-Falb定理，引入了几类稳定的分数阶Lur 'e系统。最后，为了将离轴圆判据推广到分数阶系统，给出了离轴圆判据的另一种证明方法。
英文摘要：
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.
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