scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

Stability Criterion of Discrete Hopfield Neural Networks with Multiple Delays in Parallel Mode: Linear Matrix Inequality

2011 ◽  
Vol 225-226 ◽  
pp. 1270-1273
Author(s):  
Xiao Feng Lai ◽  
Xing Yin ◽  
Hai Yang Zou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Stability Criterion ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequality ◽  
Parallel Mode

In this paper, Discrete Hopfield Neural Networks with Multple Delays is introduced.And a stability criterion of Discrete Hopfield Neural Networks with Multple Delays is studied bythe linear matrix inequality. It provides a theory basis for the application of Discrete Hopfield Neural Networks with Multple Delays.

Ultimate Boundedness of Stochastic Neural Networks with Delays

2011 ◽  
Vol 204-210 ◽  
pp. 1549-1552
Author(s):  
Li Wan ◽  
Qing Hua Zhou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Lyapunov Functional ◽  
Signal Transmission ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness

Although ultimate boundedness of several classes of neural networks with constant delays was studied by some researchers, the inherent randomness associated with signal transmission was not taken account into these networks. At present, few authors study ultimate boundedness of stochastic neural networks and no related papers are reported. In this paper, by using Lyapunov functional and linear matrix inequality, some sufficient conditions ensuring the ultimate boundedness of stochastic neural networks with time-varying delays are established. Our criteria are easily tested by Matlab LMI Toolbox. One example is given to demonstrate our criteria.

Novel Approach to Robust Stability Criteria of Uncertain System with Time-Varying Delay

2013 ◽  
Vol 631-632 ◽  
pp. 1189-1194
Author(s):  
Chao Deng ◽  
Zhao Di Xu ◽  
Yu Bai ◽  
Xin Yuan Wang
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Uncertain System ◽  
Linear Matrix ◽  
Convexity Property ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the robust stability criteria of uncertain system with time-varying delay. Firstly, by exploiting a new Lyapunov function that optimizes the segment of time delay and using the convexity property and free-weight method of the Linear Matrix Inequality, delay-dependent stability condition can be obtained for the asymptotical stability of the nominal system. Secondly, basing on the obtained condition, the corresponding linear matrix inequality can be obtained for the uncertain system. Finally, an example is given to demostrate the effectiveness and the merit of the proposed method.

Global Stability Properties for Neutral-Type Hopfield Neural Networks

2012 ◽  
Vol 232 ◽  
pp. 682-685
Author(s):  
Dao He Hao ◽  
Liang Wu
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Neutral Type ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Functional Stability ◽  
Stability Properties ◽  
Linear Matrix Inequality Approach

The global stability properties was discussed for the neutral-type Hopfield neural networks with discrete and distributed time-varying delays .Based on the Lyapunov functional stability analysis and the linear matrix inequality approach, a new sufficient condition was derived to assure the global stability properties of the equilibrium. The criterion improved and extended the results of literature, and has less conservative.

scholarly journals Dynamical Behaviors of Stochastic Hopfield Neural Networks with Both Time-Varying and Continuously Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Qinghua Zhou ◽  
Penglin Zhang ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness ◽  
Functional Theory ◽  
Dynamical Behaviors ◽  
Theoretical Results

This paper investigates dynamical behaviors of stochastic Hopfield neural networks with both time-varying and continuously distributed delays. By employing the Lyapunov functional theory and linear matrix inequality, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, an example is given to illustrate the correctness and effectiveness of our theoretical results.

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