scholarly journals Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xinsong Yang ◽  
Mengzhe Zhou ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Distributed Delay ◽  
Transmission Efficiency ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Coupled Neural Networks ◽  
Time Varying Delay ◽  
Unbounded Distributed Delays ◽  
Varying Delay

This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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 for Uncertain Neural Networks of Neutral Type with Time-Varying Delay in the Leakage Term and Distributed Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qi Zhou ◽  
Xueying Shao ◽  
Jin Zhu ◽  
Hamid Reza Karimi
Keyword(s):  
Neutral Type ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Leakage Term ◽  
Time Varying Delay ◽  
The Stability ◽  
Uncertain Networks ◽  
Varying Delay ◽  
Stability Results

The stability problem is investigated for a class of uncertain networks of neutral type with leakage, time-varying discrete, and distributed delays. Both the parameter uncertainty and the generalized activation functions are considered in this paper. New stability results are achieved by constructing an appropriate Lyapunov-Krasovskii functional and employing the free weighting matrices and the linear matrix inequality (LMI) method. Some numerical examples are given to show the effectiveness and less conservatism of the proposed results.

On Improved Delay-Range-Dependent Stability Criteria for Linear Systems with Interval Time-Varying Delay

2013 ◽  
Vol 427-429 ◽  
pp. 1306-1310
Author(s):  
Jun Jun Hui ◽  
He Xin Zhang ◽  
Fei Meng ◽  
Xin Zhou
Keyword(s):  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

In this paper, we consider the problem of robust delay-dependent stability for a class of linear uncertain systems with interval time-varying delay. By using the directly Lyapunov-Krasovskii (L-K) functional method, integral inequality approach and the free weighting matrix technique, new less conservative stability criteria for the system is formulated in terms of linear matrix inequalities .Numerical examples are given to show the effectiveness of the proposed approach.

scholarly journals Stability analysis for neural networks with discrete and leakage time-varying delay systems with delay-range-dependence and delay-derivative-dependence

2021 ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Systems Model ◽  
The Neural Networks ◽  
The Stability ◽  
Varying Delay

The paper deals with the stability problem of neural networks with discrete and leakage interval time-varying delays. Firstly, a novel Lyapunov-Krasovskii functional was constructed based on the neural networks leakage time-varying delay systems model. The delayed decomposition approach (DDA) and integral inequality techniques (IIA) were altogether employed, which can help to estimate the derivative of Lyapunov-Krasovskii functional and effectively extend the application area of the results. Secondly, by taking the lower and upper bounds of time-delays and their derivatives, a criterion on asymptotical was presented in terms of linear matrix inequality (LMI), which can be easily checked by resorting to LMI in Matlab Toolbox. Thirdly, the resulting criteria can be applied for the case when the delay derivative is lower and upper bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative characteristics. Finally, through numerical examples, the criteria will be compared with relative ones. The smaller delay upper bound was obtained by the criteria, which demonstrates that our stability criterion can reduce the conservatism more efficiently than those earlier ones.

Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay

2019 ◽  
Vol 20 (6) ◽  
pp. 623-631 ◽  
Author(s):  
Abdujelil Abdurahman ◽  
Malika Sader ◽  
Haijun Jiang
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
Mean Value ◽  
Projective Synchronization ◽  
Mean Value Theorem ◽  
Time Varying ◽  
Chaotic Neural Networks ◽  
Control Approach ◽  
Time Varying Delay ◽  
Varying Delay

AbstractCompared to other types of synchronization such as complete synchronization and lag synchronization, there is a unique advantage in projective synchronization since it can greatly improve the security of communication. In this paper, the projective synchronization problem of a class of chaotic neural networks with time-varying delay is investigated via designing a novel adaptive controller. Some simple and useful criteria are derived by employing Lyapunov functional method and Lagrange mean value theorem. Finally, an example and its numerical simulations are given to demonstrate the effectiveness of the proposed control schemes. It is worth to mention that the designed controller in this paper dos not require any knowledge about the activation functions, which can be seen the main novelty of the paper.

Delay-Dependent Robust Stability of Cellular Neural Networks with Time-Varying Discrete and Distributed Delay

2011 ◽  
Vol 50-51 ◽  
pp. 915-918
Author(s):  
Wei Wei Wang ◽  
Wei Wei Su ◽  
Yi Ming Chen
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Distributed Delay ◽  
Time Varying ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Time Varying Delay ◽  
Cross Terms ◽  
Delay Dependent ◽  
Varying Delay

Delay-dependent robust stability of neural networks with discrete and distributed delays is considered in this paper. Stability criteria are derived in LMIs avoiding bounding certain cross terms and the restriction of derivative of time-varying delay is removed. Numerical examples are given to indicate significant improvements over some existing results.

scholarly journals Exponential Stabilization of Neutral-Type Neural Networks with Interval Nondifferentiable and Distributed Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Activation Functions ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

The problem of exponential stabilization of neutral-type neural networks with various activation functions and interval nondifferentiable and distributed time-varying delays is considered. The interval time-varying delay function is not required to be differentiable. By employing new and improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, the stabilizability criteria are formulated in terms of a linear matrix inequalities. Numerical examples are given to illustrate and show the effectiveness of the obtained results.

Further Results on Exponential Robust Stability Analysis for Recurrent Neural Networks With Time-Varying Delay

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Robust Stability Analysis ◽  
The Relationship ◽  
Varying Delay

In this paper, the problems of determining the robust exponential stability and estimating the exponential convergence rate for recurrent neural networks (RNNs) with parametric uncertainties and time-varying delay are studied. The relationship among the time-varying delay, its upper bound, and their difference is taken into account. The developed stability conditions are in terms of linear matrix inequalities (LMIs) and the integral inequality approach (IIA), which can be checked easily by recently developed algorithms solving LMIs. Furthermore, the proposed stability conditions are less conservative than some recently known ones in the literature, and this has been demonstrated via four examples with simulation.

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