scholarly journals Existence, Uniqueness, and Exponential Stability of Uncertain Delayed Neural Networks with Inertial Term: Nonreduced Order Case

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. Iswarya ◽  
R. Raja ◽  
Q. Zhu ◽  
M. Niezabitowski ◽  
J. Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Inertial Term ◽  
Delayed Neural Networks ◽  
Neural Network System ◽  
Inertial Neural Networks ◽  
Inequality Techniques ◽  
The Stability ◽  
Necessary And Sufficient

In this work, we mainly focus on uncertain delayed neural network system with inertial term. Here, the existence, uniqueness, and exponential stability of inertial neural networks are derived without shifting the second order differential system into first order through substituting variables. Initially, we construct a proper Lyapunov–Krasovskii functional to investigate the stability of novel uncertain delayed inertial neural networks, which is different from the classical Lyapunov functional approach. By utilizing the Kirchhoff’s matrix tree theorem, Cauchy–Schwartz inequality, homeomorphism theorem, and some inequality techniques, the necessary and sufficient conditions are derived for the designed framework. Subsequently, to exhibit the strength of this outcome, we framed a quantitative example.

scholarly journals Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Shifang Kuang ◽  
Yunjian Peng ◽  
Feiqi Deng ◽  
Wenhua Gao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Inequality Techniques ◽  
The Stability ◽  
Stability In Mean Square

Exponential stability in mean square of stochastic delay recurrent neural networks is investigated in detail. By using Itô’s formula and inequality techniques, the sufficient conditions to guarantee the exponential stability in mean square of an equilibrium are given. Under the conditions which guarantee the stability of the analytical solution, the Euler-Maruyama scheme and the split-step backward Euler scheme are proved to be mean-square stable. At last, an example is given to demonstrate our results.

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.

ASYMPTOTIC HYPERSTABILITY OF A CLASS OF NEURAL NETWORKS

1999 ◽  
Vol 09 (02) ◽  
pp. 95-98 ◽  
Author(s):  
ANKE MEYER-BÄSE
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lyapunov Methods ◽  
Network Parameters ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Stability Results

This paper is concerned with the asymptotic hyperstability of recurrent neural networks. We derive based on the stability results necessary and sufficient conditions for the network parameters. The results we achieve are more general than those based on Lyapunov methods, since they provide milder constraints on the connection weights than the conventional results and do not suppose symmetry of the weights.

EXPONENTIAL STABILITY OF STOCHASTIC FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (10) ◽  
pp. 3387-3395 ◽  
Author(s):  
LIPING CHEN ◽  
RANCHAO WU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Equilibrium Solution ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Fuzzy Cellular Neural Networks ◽  
Mean Square Exponential Stability ◽  
Inequality Techniques

The exponential stability of a class of stochastic fuzzy cellular neural networks with distributed delays is investigated in this paper. By using analytic methods such as Lyapunov functional, Itô's formula, inequality techniques and non-negative semimartingale convergence theorem, the sufficient conditions guaranteeing the almost sure and mean square exponential stability of its equilibrium solution are respectively obtained. For illustration, an example is given to show the feasibility of results.

scholarly journals Globally Exponential Stability of Impulsive Neural Networks with Given Convergence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chengyan Liu ◽  
Xiaodi Li ◽  
Xilin Fu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Convergence Rate ◽  
Exponential Stability ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
Analysis Techniques ◽  
Globally Exponential Stability ◽  
The Stability

This paper deals with the stability problem for a class of impulsive neural networks. Some sufficient conditions which can guarantee the globally exponential stability of the addressed models with given convergence rate are derived by using Lyapunov function and impulsive analysis techniques. Finally, an example is given to show the effectiveness of the obtained results.

scholarly journals Exponential Stability for Discrete-Time Stochastic BAM Neural Networks with Discrete and Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Analysis Problem ◽  
The Stability

This paper deals with the stability analysis problem for a class of discrete-time stochastic BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and employing M-matrix theory, we find some sufficient conditions ensuring the global exponential stability of the equilibrium point for stochastic BAM neural networks with time-varying delays. The conditions obtained here are expressed in terms of LMIs whose feasibility can be easily checked by MATLAB LMI Control toolbox. A numerical example is presented to show the effectiveness of the derived LMI-based stability conditions.

scholarly journals Quantized passive filtering for switched delayed neural networks

2021 ◽  
Vol 26 (1) ◽  
pp. 93-112
Author(s):  
Youmei Zhou ◽  
Yajuan Liu ◽  
Jianping Zhou ◽  
Zhen Wang
Keyword(s):  
Neural Networks ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Passive Filter ◽  
Delayed Neural Networks ◽  
Noise Interference ◽  
Exponentially Stable ◽  
Error System ◽  
Inequality Techniques

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

scholarly journals Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

scholarly journals Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghong Lai ◽  
Tianxiang Yao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Integral Inequality ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Stability Study ◽  
Delayed Reaction ◽  
Regional Features ◽  
The Stability

This work is devoted to the stability study of impulsive cellular neural networks with time-varying delays and reaction-diffusion terms. By means of new Poincaré integral inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some novel and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and show that not only the reaction-diffusion coefficients but also the regional features including the boundary and dimension of spatial variable can influence the stability. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.

scholarly journals Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Quan Xu ◽  
Jibin Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Complex Valued

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

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