Converse Lyapunov Theorem for Nabla Asymptotic Stability Without Conservativeness

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作者：
School of Mathematics, Southeast University, Nanjing [1 ]
211189, China
不详 [2 ]
CA
95343, United States
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来源：
IEEE Trans. Syst. Man Cybern. Syst. | 2022年 / 4卷 / 2676-2687期
关键词：
Asymptotically stable - Converse Lyapunov theorem - First order differences - Fractional-order systems - Indirect methods - Linear time invariant - Positive definite lyapunov functions;
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摘要：
This article focuses on the conservativeness issue of the existing Lyapunov method for linear time-invariant (LTI) nabla fractional-order systems and proposes a converse Lyapunov theorem to overcome the conservative problem. It is shown that the LTI nabla fractional-order system is asymptotically stable if and only if there exist a positive-definite Lyapunov function whose first-order difference is negative definite. After developing a systematic scheme to construct such Lyapunov candidates, the Lyapunov indirect method is derived for the nonlinear system. Finally, the effectiveness and practicability of the proposed methods are substantiated with four examples. © 2013 IEEE.
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