New Criteria on Finite-Time Stability of Fractional-Order Hopfield Neural Networks With Time Delays

Du, Feifei; Lu, Jun‐Guo

doi:10.1109/tnnls.2020.3016038

Cited by 49 publications

(22 citation statements)

References 55 publications

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“…at the equilibrium point E(0, 0) the characteristic polynomial of the matrix −C + BJ is given by ∆(λ) = λ 7 + 0.65λ 4 0.525λ 3 + 0.5325 (11) The roots λi's and their appropriate arguments of polynomial of ( 11 Numerical solution of the incommensurate neorder neural networks (9) Since…”

Section: Examplementioning

confidence: 99%

“…For time step size 0.01 and initial value x0 = [10, −10] T , numerical simulation results in Figure 1 illustrate the asymptotically stability of system (9) for the given fractional-orders.…”

Section: Examplementioning

confidence: 99%

“…To its memory and heredity features, for that fractional-order neural networks are projected to be particularly useful in many applications [6]. It is also shown that fractional-order neural networks may be successfully employed in a variety of study domains [14] [4].Strong requirements have been offered for commensurate fractional order neural networks (including derivation orders that are all multiples of the same order), in [27] Global asymptotic stability of fractional-order competitive neural networks with multiple time-varying-delay links was investigated, Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field was adressed in [3], and in [9], New criteria on finite-time stability of fractional-order hopfield neural networks with time delays was introduced, [15] treated α-stability and α-synchronization for fractional-order neural networks.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability analysis and synchronization of incommensurate fractional-order neural netwroks

Hioual

Oussaeif²

2022

IJM

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This paper develops a theoretical framework for analyzing the stability of nonlinear incommensurate fractional- order neural networks. A necessary theorem for asymptotical stability is established using the characteristic equation for a nonlinear fractional-order system, and how to employ this theorem in stabilization is also presented. With the suitable control, the difficulties of stabilization and synchronization of fractional-order chaotic incommensurate fractional-order neural networks may be readily overcome. Two numerical examples have been shown to demonstrate how the established theory may be used to investigate stability and construct stabilization controllers.

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Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability analysis and synchronization of incommensurate fractional-order neural netwroks

Hioual

Oussaeif²

2022

IJM

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“…Remark 3.7 It is noted that for a nonnegative function f (t), the fractional integral t 0 (ts) α 1 -α 2 -1 f (s) ds may be monotonically increasing or decreasing with respect to t for 0 < α 1α 2 < 1 (see [3,9,11,30]). To prove that the integral term t 0 (ts) α 1 -α 2 -1 f (s) ds is monotonically increasing for f (t) ≥ 0, there is an alternative approach found in [10] (Lemma 5).…”

Section: Corollary 36mentioning

confidence: 99%

“…Zhang et al [44] discussed the stability concept for fractional nonlinear systems with order from (0, 2). In [8], FTS analysis of delayed nonlinear fractional difference system was investigated by using Gronwall and Jensen inequalities, and the same concept was discussed for a Hopfield neural network with time delay in [11]. In [10], the authors studied FTS of delayed fractional neutral systems by using Gronwall inequality.…”

Section: Introductionmentioning

confidence: 99%

Finite-time stability of multiterm fractional nonlinear systems with multistate time delay

Arthi¹,

Brindha²,

2021

Adv Differ Equ

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This work is mainly concentrated on finite-time stability of multiterm fractional system for $0 < \alpha _{2} \leq 1 < \alpha _{1} \leq 2$ 0 < α 2 ≤ 1 < α 1 ≤ 2 with multistate time delay. Considering the Caputo derivative and generalized Gronwall inequality, we formulate the novel sufficient conditions such that the multiterm nonlinear fractional system is finite time stable. Further, we extend the result of stability in the finite range of time to the multiterm fractional integro-differential system with multistate time delay for the same order by obtaining some inequality using the Gronwall approach. Finally, from the examples, the advantage of presented scheme can guarantee the stability in the finite range of time of considered systems.

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Finite difference based iterative learning control with initial state learning for a class of fractional order two‐dimensional continuous‐discrete linear systems

Lan

Zheng

2022

Adaptive Control & Signal

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This article presents a PI-type iterative learning control (ILC) law with initial state learning for a class of 𝛼 (0 < 𝛼 ≤ 1) fractional order two-dimensional (2D) linear systems. First, by using backward difference method, the finite difference approximation of the fractional order derivative is obtained, which leads to globally 2 − 𝛼 order accuracy. Then, a PI-ILC law is constructed at the nodes and the convergence analysis of the iterative scheme is proved. A linear matrix inequality-based sufficient condition is derived to guarantee that the tracking error is asymptotically convergent. The obtained convergence condition is fractional order dependent. Most of the classical ILC conditions for fractional order one-dimensional linear systems fall into the special cases of this article. Finally, the simulation results show the effectiveness of the proposed control method.

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New Criteria on Finite-Time Stability of Fractional-Order Hopfield Neural Networks With Time Delays

Cited by 49 publications

References 55 publications

Stability analysis and synchronization of incommensurate fractional-order neural netwroks

Stability analysis and synchronization of incommensurate fractional-order neural netwroks

Finite-time stability of multiterm fractional nonlinear systems with multistate time delay

Finite difference based iterative learning control with initial state learning for a class of fractional order two‐dimensional continuous‐discrete linear systems

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