Global dissipativity and finite-time synchronization of mixed time-varying delayed memristor-based neural networks with discontinuous activations

2021 ◽  
Vol 40 (1) ◽  
pp. 1695-1712
Author(s):  
Kaifang Fei ◽  
Minghui Jiang ◽  
Yadan Zhang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Matrix Measure ◽  
Feedback Controllers ◽  
Discontinuous Activations ◽  
Inclusion Theory ◽  
Generalized Halanay Inequality

In this paper, the matters of dissipativity and finite time synchronization for memristor-based neural networks (MNNs) with mixed time-varying discontinuities are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. Then, the global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, some novel sufficient conditions are introduced to guarantee the finite-time synchronization of the drive-response MNNs based on a simple Lyapunov function and two different feedback controllers. Finally, several numerical examples are given to verify the validity of the theoretical results.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 693-704 ◽  
Author(s):  
Kaifang Fei ◽  
Minghui Jiang ◽  
Meng Yan ◽  
Weizhen Liu
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Exponential Synchronization ◽  
Matrix Measure ◽  
Analysis Techniques ◽  
Discontinuous Activations ◽  
Inclusion Theory ◽  
Generalized Halanay Inequality ◽  
New Criteria ◽  
Theoretical Results

AbstractIn this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

Finite-time Synchronization of fractional-order complex-valued fuzzy cellular neural networks with time-varying delays

2021 ◽  
pp. 1-11
Author(s):  
Wenbin Jin ◽  
Wenxia Cui ◽  
Zhenjie Wang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Order Complex ◽  
Fuzzy Cellular Neural Networks ◽  
Complex Valued

Finite-time synchronization is concerned for the fractional-order complex-valued fuzzy cellular neural networks (FOCVFCNNs) with leakage delay and time-varying delays. Without using the usual complex-valued system decomposition method, this paper designs the different forms of the controllers by using 2-norm. And we construct the appropriate Lyapunov functional and apply inequality analytical techniques, some new sufficient conditions are obtained to ensure finite-time synchronization of the FOCVFCNNs. The upper bound of setting-time function is obtained. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results.

scholarly journals Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

2018 ◽  
Vol 23 (4) ◽  
pp. 515-532
Author(s):  
Yujiao Liu ◽  
Xiaoxiao Wan ◽  
Enli Wu ◽  
Xinsong Yang ◽  
Fuad E. Alsaadi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Analytical Techniques ◽  
Settling Time ◽  
Proportional Delay ◽  
Sign Function ◽  
Proportional Delays ◽  
Discontinuous Activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results.

scholarly journals Finite-time synchronization problem of a class of discontinuous Cohen–Grossberg neural networks with mixed delays via new switching design

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhaohong Xiang ◽  
Runjie Li
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Control Approach ◽  
Synchronization Problem ◽  
Analysis Theory ◽  
Discontinuous Activations ◽  
Discontinuous Activation Functions

AbstractThis paper investigates a class of generalized Cohen–Grossberg neural networks (CGNNs) with discontinuous activations and mixed delays. Based on the nonsmooth analysis theory, the drive-response concept, differential inclusions theory, we give several basic assumptions to gain the finite-time synchronization issue of CGNNs. Sufficient conditions are provided without the boundedness or monotonicity of discontinuous activation functions. Moreover, one can estimate the settling time’s upper bounds of the system. At last, two numerical examples and their simulations are given to further show the benefits of the obtained control approach.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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