scholarly journals Input-to-State Stability of Stochastic Memristive Neural Networks with Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xu Y. Lou ◽  
Qian Ye
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Mean Square ◽  
Memristive Neural Networks ◽  
Time Varying Delay ◽  
Analysis Theory ◽  
Mean Square Exponential Stability ◽  
The Neural Networks ◽  
Varying Delay

This paper is concerned with the input-to-state stability problem of a class of memristive neural networks. We consider the neural networks that take into account both the stochastic effects and time-varying delay, and introduce the notions of meansquare exponential input-to-state stability. Using the stochastic analysis theory and Itô formula for stochastic differential equations, we establish sufficient conditions for both mean-square exponential input-to-state stability and mean-square exponential stability. Numerical simulations are also provided to demonstrate the theoretical results.

Mean-Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 1742-1747
Author(s):  
Jin Fang Han
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Mean Square ◽  
Razumikhin Theorem ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Varying Delay

This paper is concerned with the mean-square exponential stability analysis problem for a class of stochastic interval cellular neural networks with time-varying delay. By using the stochastic analysis approach, employing Lyapunov function and norm inequalities, several mean-square exponential stability criteria are established in terms of the formula and Razumikhin theorem to guarantee the stochastic interval delayed cellular neural networks to be mean-square exponential stable. Some recent results reported in the literatures are generalized. A kind of equivalent description for this stochastic interval cellular neural networks with time-varying delay is also given.

Fixed-time synchronization of quaternion-valued neural networks with time-varying delay

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200324
Author(s):  
Umesh Kumar ◽  
Subir Das ◽  
Chuangxia Huang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
Time Varying ◽  
Activation Functions ◽  
Time Varying Delay ◽  
The Neural Networks ◽  
Varying Delay

In this article, sufficient conditions for fixed-time synchronization of time-delayed quaternion-valued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four real-valued systems. Then using the available lemmas and by constructing the Lyapunov function, the synchronization criterion for the neural networks is proposed. Activation functions satisfy the Lipschitz condition. A suitable controller has been designed to synchronize the master–slave systems. The effectiveness of the proposed result is validated through a comparison of the settling time obtained by applying two different existing lemmas to a particular problem of synchronization of two identical QVNNs with time-varying delay with the help of suitable controllers.

scholarly journals Stability Analysis for Stochastic Neutral-Type Memristive Neural Networks with Time-Varying Delay and S-Type Distributed Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Changjian Wang ◽  
Zuoliang Xiong ◽  
Min Liang ◽  
Hongwei Yin
Keyword(s):  
Neural Networks ◽  
Stochastic Analysis ◽  
Neutral Type ◽  
Distributed Delays ◽  
Time Varying ◽  
Memristive Neural Networks ◽  
Time Varying Delay ◽  
System A ◽  
Analysis Theory ◽  
Varying Delay

In this paper, we consider the input-to-stability for a class of stochastic neutral-type memristive neural networks. Neutral terms and S-type distributed delays are taken into account in our system. Using the stochastic analysis theory and Itô formula, we obtain the conditions of mean-square exponential input-to-stability for system. A numerical example is given to illustrate the correctness of our conclusions.

scholarly journals Finite-time Stabilization for Uncertain Neural Networks With Time-varying Delay

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Control Design ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Neural Networks ◽  
Finite Time Boundedness ◽  
And Control ◽  
Varying Delay

In this paper, the problems of finite-time boundedness and control design for uncertain neuralnetworks with time-varying delay is considered. By constructing Lyapunov-Krasovskii function and using thematrix inequality method, sufficient conditions for finite-time boundedness of a class of neural networks withtime-varying delay are established. Then, we proposed a criterion to ensure that the neural networks with timevarying delay is finite-time stabilizable. A numerical example is given to verify the validity of the results.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Stability Analysis and RobustH∞Control of Switched Stochastic Systems with Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhengrong Xiang ◽  
Guoxin Chen
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Time Varying Delay ◽  
Switched Stochastic Systems ◽  
Mean Square Exponential Stability ◽  
Varying Delay

The problems of mean-square exponential stability and robustH∞control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then,H∞performance is studied and robustH∞controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

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