scholarly journals Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Sundaram Senthilraj ◽  
Ramachandran Raja ◽  
Jinde Cao ◽  
Habib M. Fardoun
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Randomly Occurring Uncertainties ◽  
Fuzzy Neural ◽  
Delay Partitioning ◽  
Dissipativity Analysis

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results.

A DELAY-DEPENDENT APPROACH TO ROBUST PASSIVITY ANALYSIS FOR TAKAGI-SUGENO FUZZY UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2013 ◽  
Vol 21 (03) ◽  
pp. 415-433 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Passivity Analysis ◽  
Fuzzy Neural ◽  
Delay Dependent

This paper deals with the passivity analysis problem for Takagu-Sugeno (T-S) fuzzy neural networks with mixed interval time-varying delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Delay-dependent sufficient conditions for the passivity problem are obtained by using Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique. The important feature of the results lies in that it does not make use of upper bounds to introduce some degree of conservativeness. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design procedures.

scholarly journals Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
YaJun Li ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
The Novel ◽  
Free Weight ◽  
Fuzzy Neural ◽  
The Stability

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

scholarly journals Passivity analysis of multiple time-varying time delayed complex variable neural networks in finite-time

2021 ◽  
Vol 8 (4) ◽  
pp. 842-854
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Valued ◽  
Theoretical Results

In this article, we investigate the problem of finite-time passivity for the complex-valued neural networks (CVNNs) with multiple time-varying delays. To begin, many definitions relevant to the finite-time passivity of CVNNs are provided; then the suitable control inputs are designed to guarantee the class of CVNNs are finite-time passive. In the meantime, some sufficient conditions of linear matrix inequalities (LMIs) are derived by using inequalities techniques and Lyapunov stability theory. Finally, a numerical example is presented to illustrate the usefulness of the theoretical results.

GLOBAL SYNCHRONIZATION IN AN ARRAY OF DISCRETE-TIME NEURAL NETWORKS WITH NONLINEAR COUPLING AND TIME-VARYING DELAYS

2009 ◽  
Vol 19 (01) ◽  
pp. 57-63 ◽  
Author(s):  
JINLING LIANG ◽  
ZIDONG WANG ◽  
XIAOHUI LIU
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Coupled Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Coupling ◽  
Global Synchronization ◽  
Synchronization Scheme

A general model for an array of discrete-time neural networks with hybrid coupling is proposed, which is composed of nonlinear coupling and time-varying delays. The coupling terms are described in terms of Lipchitz-type conditions that reflect more realistic dynamical behaviors of coupled systems in practice. The properties of Kronecker product are employed in order to pursue mathematical simplicity of dynamics analysis. On the basis of Lyapunov stability theory, an effective matrix functional is utilized to establish sufficient conditions under which the considered neural networks are globally synchronized. These conditions, which are dependent on the lower bound and the upper bound of the time-varying time delays, are expressed in terms of several linear matrix inequalities (LMIs), and therefore can be easily verified by utilizing the numerically efficient Matlab LMI toolbox. One illustrative example is given to justify the validity and feasibility of the proposed synchronization scheme.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of 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.

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