Asymptotical stability and asymptotic periodicity for the Lasota-Wazewska model of fractional order with infinite delays

In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.

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Robust asymptotical stability of fractional-order linear systems with structured perturbations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2013.03.001 ◽

2013 ◽

Vol 66 (5) ◽

pp. 873-882 ◽

Cited By ~ 17

Author(s):

Jun-Guo Lu ◽

Yangquan Chen ◽

Weidong Chen

Keyword(s):

Linear Systems ◽

Fractional Order ◽

Asymptotical Stability ◽

Order Linear ◽

Structured Perturbations

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Robust stability bounds of uncertain fractional-order systems

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0159-3 ◽

2014 ◽

Vol 17 (1) ◽

Cited By ~ 10

Author(s):

YingDong Ma ◽

Jun-Guo Lu ◽

WeiDong Chen ◽

YangQuan Chen

Keyword(s):

Fractional Order ◽

Robust Stability ◽

Asymptotical Stability ◽

Asymptotically Stable ◽

Fractional Order Systems ◽

Infinity Norm ◽

Stability Bound ◽

Bounded Uncertainty ◽

Theoretical Results

AbstractThis paper considers the robust stability bound problem of uncertain fractional-order systems. The system considered is subject either to a two-norm bounded uncertainty or to a infinity-norm bounded uncertainty. The robust stability bounds on the uncertainties are derived. The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractional-order systems are already asymptotically stable. Simulation examples are given to demonstrate the effectiveness of the proposed theoretical results.

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Asymptotical Stability of Riemann–Liouville Fractional-Order Neutral-Type Delayed Projective Neural Networks

Neural Processing Letters ◽

10.1007/s11063-019-10050-8 ◽

2019 ◽

Vol 50 (1) ◽

pp. 565-579 ◽

Cited By ~ 1

Author(s):

Jin-dong Li ◽

Zeng-bao Wu ◽

Nan-jing Huang

Keyword(s):

Neural Networks ◽

Fractional Order ◽

Neutral Type ◽

Asymptotical Stability

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Asymptotical stability of fractional order systems with time delay via an integral inequality

IET Control Theory and Applications ◽

10.1049/iet-cta.2017.1144 ◽

2018 ◽

Vol 12 (12) ◽

pp. 1748-1754 ◽

Cited By ~ 26

Author(s):

Bin-Bin He ◽

Hua-Cheng Zhou ◽

YangQuan Chen ◽

Chun-Hai Kou

Keyword(s):

Time Delay ◽

Fractional Order ◽

Integral Inequality ◽

Asymptotical Stability ◽

Fractional Order Systems

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Robust Asymptotical Stability and Stabilization of Fractional-Order Complex-Valued Neural Networks with Delay

Discrete Dynamics in Nature and Society ◽

10.1155/2021/5653791 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Jingjing Zeng ◽

Xujun Yang ◽

Lu Wang ◽

Xiaofeng Chen

Keyword(s):

Neural Networks ◽

Time Delay ◽

Fractional Order ◽

Asymptotical Stability ◽

Order Complex ◽

Practical Application ◽

Stability And Stabilization ◽

Complex Valued ◽

Fractional Orders ◽

Theoretical Results

The robust asymptotical stability and stabilization for a class of fractional-order complex-valued neural networks (FCNNs) with parametric uncertainties and time delay are considered in this paper. It is worth noting that our system combines complex numbers, uncertain parameters, time delay, and fractional orders, which is universal in practical application. Using the theorem of homeomorphism, the sufficient condition of the existence and uniqueness of the equilibrium point for the system is obtained. Then, the sufficient criteria of robust asymptotical stability and stabilization for the addressed models are established, respectively. Finally, we give two numerical examples to verify the feasibility and effectiveness of the theoretical results.

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