LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

Zhang, Hai; Ye, Renyu; Liu, Song; Cao, Jinde; Alsaedi, A.; Li, Xiaodi

doi:10.1080/00207721.2017.1412534

Cited by 64 publications

(15 citation statements)

References 38 publications

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“…To solve this BMI, we can use the branch and bound methods proposed in [40] or the homotopy‐based algorithm in [41]. Remark 5 It is worth noting that to apply the fractional stability Lyapunov theorem, the proposed L–K functional

V false(t, x_{t} false)

must be positive definite, however, the authors of [42, 43] proposed L–K functional

V false(t, x_{t} false) = I^{α} false(x^{normalT} false(t false) P x false(t false) false) + \int_{t - h false(t false)}^{t} x^{normalT} false(s false) Q x false(s false) d s, P > 0, Q > 0,

which is obviously not positive definite: the first functional

I^{α} false(x^{normalT} false(t false) P x false(t false) false)

is non‐negative, the second functional

\int_{t - h false(t false)}^{t} x^{normalT} false(s false) Q x false(s false) d s

is obviously not greater than

λ ∥ x false(t false) ∥^{2}

, for some

λ > 0

. Therefore, the use of the fractional stability theorem for system (1) in these papers is incorrect.…”

Section: Resultsmentioning

confidence: 99%

Switching law design for finite‐time stability of singular fractional‐order systems with delay

Thành¹,

Phát

2019

IET Control Theory & Applications

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V false(t, x_{t} false)

must be positive definite, however, the authors of [42, 43] proposed L–K functional

V false(t, x_{t} false) = I^{α} false(x^{normalT} false(t false) P x false(t false) false) + \int_{t - h false(t false)}^{t} x^{normalT} false(s false) Q x false(s false) d s, P > 0, Q > 0,

which is obviously not positive definite: the first functional

I^{α} false(x^{normalT} false(t false) P x false(t false) false)

is non‐negative, the second functional

\int_{t - h false(t false)}^{t} x^{normalT} false(s false) Q x false(s false) d s

is obviously not greater than

λ ∥ x false(t false) ∥^{2}

, for some

λ > 0

. Therefore, the use of the fractional stability theorem for system (1) in these papers is incorrect.…”

Section: Resultsmentioning

confidence: 99%

Switching law design for finite‐time stability of singular fractional‐order systems with delay

Thành¹,

Phát

2019

IET Control Theory & Applications

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“…In [39,40], the authors considered the global Mittag-Leffler stability and the global exponential stability for Caputo fractional-order neural network with discrete and infinitetime distributed delays. Recently, Zhang et al [41] investigated the asymptotic stability for a class of Riemann-Liouville fractional-order neural networks with discrete and finite-time distributed constant delays. In [42], Wu et al studied the uniform stability of Caputo fractionalorder neural networks with discrete and finite-time distributed constant delays.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays

Yang

Zhang

2019

Complexity

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This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

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“…Furthermore, for drive-response FNNs, it is critical to design some kinds of control laws in order to ensure the synchronization between the drive and response ones. Recently, a great deal of outstanding results about the stability, the robust stability and synchronization of FNNs were obtained [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In [16], α-stability and α-synchronization were investigated for FNNs.…”

Section: Introductionmentioning

confidence: 99%

LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks

Lin

Chen

et al. 2019

Adv Differ Equ

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This paper addresses the issue of three dynamical behaviors including global Mittag-Leffler stability, robust stability and projection synchronization for fractional-order quaternion-valued neural networks (FQVNNs). Some linear matrix inequality conditions for these dynamical behaviors of FQVNNs are given by Lyapunov stability theory, quaternion matrix theory, Homeomorphic mapping theory and fractional differential equation theory. Furthermore, these obtained sufficient conditions for stability and synchronization are superior to those in existing literature. Finally, three examples are given to illustrate the effectiveness of the theoretical results.

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LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

Cited by 64 publications

References 38 publications

Switching law design for finite‐time stability of singular fractional‐order systems with delay

Switching law design for finite‐time stability of singular fractional‐order systems with delay

Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays

LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks

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