scholarly journals Discrete-Time Stochastic Quaternion-Valued Neural Networks with Time Delays: An Asymptotic Stability Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 936 ◽  
Author(s):  
Ramalingam Sriraman ◽  
Grienggrai Rajchakit ◽  
Chee Peng Lim ◽  
Pharunyou Chanthorn ◽  
Rajendran Samidurai
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
System Modeling ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Mean Square ◽  
Stochastic Disturbances ◽  
Stability Issue ◽  
The Mean

Stochastic disturbances often cause undesirable characteristics in real-world system modeling. As a result, investigations on stochastic disturbances in neural network (NN) modeling are important. In this study, stochastic disturbances are considered for the formulation of a new class of NN models; i.e., the discrete-time stochastic quaternion-valued neural networks (DSQVNNs). In addition, the mean-square asymptotic stability issue in DSQVNNs is studied. Firstly, we decompose the original DSQVNN model into four real-valued models using the real-imaginary separation method, in order to avoid difficulties caused by non-commutative quaternion multiplication. Secondly, some new sufficient conditions for the mean-square asymptotic stability criterion with respect to the considered DSQVNN model are obtained via the linear matrix inequality (LMI) approach, based on the Lyapunov functional and stochastic analysis. Finally, examples are presented to ascertain the usefulness of the obtained theoretical results.

scholarly journals Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Chuangxia Huang ◽  
Jie Cao ◽  
Peng Wang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Ultimate Boundedness ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Uniformly Ultimate Boundedness

We address the problem of stochastic attractor and boundedness of a class of switched Cohen-Grossberg neural networks (CGNN) with discrete and infinitely distributed delays. With the help of stochastic analysis technology, the Lyapunov-Krasovskii functional method, linear matrix inequalities technique (LMI), and the average dwell time approach (ADT), some novel sufficient conditions regarding the issues of mean-square uniformly ultimate boundedness, the existence of a stochastic attractor, and the mean-square exponential stability for the switched Cohen-Grossberg neural networks are established. Finally, illustrative examples and their simulations are provided to illustrate the effectiveness of the proposed results.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

2017 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Qimin Zhang ◽  
Xinjing Zhang ◽  
Hongfu Yang
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Volterra System ◽  
Feedback Controls ◽  
The Mean

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

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.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Mean-Square Exponential Synchronization of Stochastic Complex Dynamical Networks with Switching Topology by Impulsive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xuefei Wu ◽  
Chen Xu
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Linear Matrix ◽  
Mean Square ◽  
Dynamical Networks ◽  
The Mean ◽  
Networks With Switching Topology

This paper investigates the mean-square exponential synchronization issues of delayed stochastic complex dynamical networks with switching topology and impulsive control. By using the Lyapunov functional method, impulsive control theory, and linear matrix inequality (LMI) approaches, some sufficient conditions are derived to guarantee the mean-square exponential synchronization of delay complex dynamical network with switch topology, which are independent of the network size and switch topology. Numerical simulations are given to illustrate the effectiveness of the obtained results in the end.

scholarly journals On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

scholarly journals Stability of Stochastic Discrete-Time Neural Networks with Discrete Delays and the Leakage Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Liyuan Hou ◽  
Hong Zhu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Delays ◽  
The Stability

This paper investigates the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay. As the partition of time-varying and leakage delay is brought in the discrete-time system, we construct a novel Lyapunov-Krasovskii function based on stability theory. Furthermore sufficient conditions are derived to guarantee the global asymptotic stability of the equilibrium point. Numerical example is given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

NOVEL STABILITY CRITERIA ON DISCRETE-TIME NEURAL NETWORKS WITH BOTH TIME-VARYING AND DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (04) ◽  
pp. 269-283 ◽  
Author(s):  
TAO LI ◽  
AIGUO SONG ◽  
SHUMIN FEI
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Combination Methods

This paper investigates robust exponential stability for discrete-time recurrent neural networks with both time-varying delay (0 ≤ τm ≤ τ(k) ≤ τM) and distributed one. Through partitioning delay intervals [0,τm] and [τm,τM], respectively, and choosing an augmented Lyapunov-Krasovskii functional, the delay-dependent sufficient conditions are obtained by using free-weighting matrix and convex combination methods. These criteria are presented in terms of linear matrix inequalities (LMIs) and their feasibility can be easily checked by resorting to LMI in Matlab Toolbox in Ref. 1. The activation functions are not required to be differentiable or strictly monotonic, which generalizes those earlier forms. As an extension, we further consider the robust stability of discrete-time delayed Cohen-Grossberg neural networks. Finally, the effectiveness of the proposed results is further illustrated by three numerical examples in comparison with the reported ones.

scholarly journals Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Ling Hou ◽  
Dongyan Chen ◽  
Chan He
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Existence Condition ◽  
Mode Switching ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Time Varying Delay ◽  
Mixed Time Delays

This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discrete-time neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays. First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. Then, the main results are extended to SFTD control. Furthermore, existence condition of nonfragile controller is derived based on solution of linear matrix inequalities (LMIs). Finally, two numerical examples are employed to show the effectiveness of the obtained methods.

scholarly journals Asymptotic Behavior of Switched Stochastic Delayed Cellular Neural Networks via Average Dwell Time Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hanfeng Kuang ◽  
Jinbo Liu ◽  
Xi Chen ◽  
Jie Mao ◽  
Linjie He
Keyword(s):  
Neural Networks ◽  
Asymptotic Behavior ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Cellular Neural Networks ◽  
Mixed Delays ◽  
Time Varying ◽  
Mean Square ◽  
The Mean

The asymptotic behavior of a class of switched stochastic cellular neural networks (CNNs) with mixed delays (discrete time-varying delays and distributed time-varying delays) is investigated in this paper. Employing the average dwell time approach (ADT), stochastic analysis technology, and linear matrix inequalities technique (LMI), some novel sufficient conditions on the issue of asymptotic behavior (the mean-square ultimate boundedness, the existence of an attractor, and the mean-square exponential stability) are established. A numerical example is provided to illustrate the effectiveness of the proposed results.

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