Robust state estimation for fractional-order delayed BAM neural networks via LMI approach

Nagamani, G.; Shafiya, M.; Soundararajan, G.; Prakash, M. Arun

doi:10.1016/j.jfranklin.2020.01.028

Cited by 32 publications

(15 citation statements)

References 33 publications

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“…In [35], the global stability condition of the fractional-order neural network is given by using the LMI method, but the time delay is not discussed. In [38], the state estimation of FOBAM neural network is studied by using fractional Lyapunov direct method and LMI method. Inspired by [34]- [36], Theorem 2 combines Lyapunov method with LMI method to propose a stability criterion for fractional-order neural network with time delay.…”

Section: B N -Dimensional Fractional-order Neural Network With Delaymentioning

confidence: 99%

“…Based on the above analysis, although there are many research results on the stability of fractional-order neural networks [34]- [39], the existing research results still face many difficulties. For example, the practical application environment of fractional-order systems is not clear [34], [35], the suitable field is not wide enough [36], [37], and there are many constraints on the stability criteria [38], [39]. At the same time, because the fractional calculus does not meet the Leibniz law, as a result, the stability criterion of a fractionalorder system cannot be directly applied to the analysis of a high-dimensional system [38].…”

Section: Introductionmentioning

confidence: 99%

“…For example, the practical application environment of fractional-order systems is not clear [34], [35], the suitable field is not wide enough [36], [37], and there are many constraints on the stability criteria [38], [39]. At the same time, because the fractional calculus does not meet the Leibniz law, as a result, the stability criterion of a fractionalorder system cannot be directly applied to the analysis of a high-dimensional system [38]. To develop a more concise and effective stability analysis method for fractional-order neural networks, we need to further study new stability criteria of fractional-order neural networks.…”

Section: Introductionmentioning

confidence: 99%

“…(1) The LMI is an effective method for the stability analysis of integer-order systems and has been successfully extended to fractionalorder systems. In [34], [35], [38], LMI stability criteria for fractional-order nonlinear systems are established and used for analyzing the global Mittag-Leffler stability of fractionalorder neural networks [34]. By using a positive definite quadratic Lyapunov function, the global Mittag-Leffler stability criterion with impulsive effects is obtained in LMI form.…”

Section: Introductionmentioning

confidence: 99%

“…Fractional-order neural network analysis based on LMI has the advantages of clear expression, simple calculation and strong practicability [35]. Therefore, the stability analysis of fractional-order systems based on LMI has received increasing attention from experts in this field [38]. (2) The Lyapunov direct method is a method that can determine the equilibrium point and judge the stability of the system without solving equations [29], [35].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method

Chang

Zhu

et al. 2021

IEEE Access

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At present, the theory and application of fractional-order neural networks remain in the exploratory stage. We study the asymptotic stability of fractional-order neural networks with Riemann-Liouville (R-L) derivatives. For non-delayed and delayed systems, we propose an asymptotic stability criterion based on the combination of the Lyapunov method and linear matrix inequality (LMI) method. The highlights include the following: (1) for fractional-order neural networks with time delay, the existence and uniqueness of solutions are proven by using matrix analysis theory and contraction mapping theorem, and (2) based on the unique solution, a suitable Lyapunov functional is constructed. Based on the inequality theorem and LMI method, two sets of asymptotic stability criteria for fractional-order neural networks are proven, which avoids the difficulty of solving the fractional derivative by the Leibniz law. Finally, the results are verified using numerical simulations.INDEX TERMS fractional-order neural networks, time delay, asymptotic stability, Lyapunov, LMI

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Section: B N -Dimensional Fractional-order Neural Network With Delaymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method

Chang

Zhu

et al. 2021

IEEE Access

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Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

Wang

Zhou

Shi

et al. 2022

Optim Control Appl Methods

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The robust control for uncertain variable fractional order time‐varying delayed differential systems with nonlinear perturbations are concerned in this article. Firstly, by introducing a novel form of the control law which is inspired by the sliding mode design, a new state feedback controller is built. Besides, a specific and comprehensive Lyapunov–Krasovskii function is adopted to deduce the sufficient conditions for the stability and robust stabilization of the system by using some linear matrix inequalities. In addition, the controller gain matrix can also be derived from the point of stability. Finally, two comparison examples are presented to demonstrate the effectiveness of the proposed control technique. The simulation results show that this method can make the state variables converge to the steady ones more quickly and stably.

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Synchronization of Delayed Fractional-Order Memristive BAM Neural Networks

Shafiya

Nagamani

2021

Springer Proceedings in Mathematics &Amp; Statistics

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Robust state estimation for fractional-order delayed BAM neural networks via LMI approach

Cited by 32 publications

References 33 publications

Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method

Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method

Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

Synchronization of Delayed Fractional-Order Memristive BAM Neural Networks

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