scholarly journals Delay-Dependent State Estimation of Static Neural Networks with Time-Varying and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Lei Shao ◽  
He Huang ◽  
Heming Zhao ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Lyapunov Functional ◽  
Estimation Error ◽  
Time Derivative ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Static Neural Networks

This paper focuses on studying the state estimation problem of static neural networks with time-varying and distributed delays. By constructing a suitable Lyapunov functional and employing two integral inequalities, a sufficient condition is obtained under which the estimation error system is globally asymptotically stable. It can be seen that this condition is dependent on the two kinds of time delays. To reduce the conservatism of the derived result, Wirtinger inequality is employed to handle a cross term in the time-derivative of Lyapunov functional. It is further shown that the design of the gain matrix of state estimator is transformed to finding a feasible solution of a linear matrix inequality, which is efficiently facilitated by available algorithms. A numerical example is explored to demonstrate the effectiveness of the developed result.

scholarly journals State Estimation for Neural Networks with Leakage Delay and Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jing Liang ◽  
Zengshun Chen ◽  
Qiankun Song
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Time Varying Delay ◽  
General Activation ◽  
Delay Dependent ◽  
Error State

The state estimation problem is investigated for neural networks with leakage delay and time-varying delay as well as for general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing matrix inequality techniques, a delay-dependent linear matrix inequalities (LMIs) condition is developed to estimate the neuron state with some observed output measurements such that the error-state system is globally asymptotically stable. An example is given to show the effectiveness of the proposed criterion.

scholarly journals Robust H-infinity State Estimation of Uncertain Neural Networks with Two Additive Time-Varying Delays

2020 ◽  
Author(s):  
Xiaoping Hu ◽  
Yajun Wang ◽  
Jiakai Ding ◽  
Dongming Xiao
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
H Infinity ◽  
Uncertain Neural Networks ◽  
Error System

This study is mainly concerned with the problem of robust H∞ state estimation of uncertain neural networks with two additive time-varying delays. A novel linear matrix inequalities (LMIs) is constructed based on Lyapunov-Krasovskii functionals (LKFs) which contains two additive time-varying delays components. LMIs method are used to estimate the derivative of LKFs, it is calculated that the derivative of the LKFs is smaller than zero, which proved that uncertain neural networks with two additive time-varying delays is globally asymptotically stable. Meantime, a stability criterion of error system is presented such that the HâĹđ performance is guaranteed. Finally, two numerical simulation examples have been performed to demonstrate the effectiveness of developed approach.

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.

scholarly journals Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Hongwen Xu ◽  
Huaiqin Wu ◽  
Ning Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
State Estimation ◽  
Time Delays ◽  
Estimation Error ◽  
Linear Matrix ◽  
Robust Exponential Stability ◽  
Interval Neural Networks ◽  
Distributed Time Delays ◽  
Error System

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

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