scholarly journals Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Yingwei Li ◽  
Huaiqin Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Activation Functions ◽  
Markovian Jump ◽  
Delayed Neural Networks ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays ◽  
Finite State

The exponential stability issue for a class of stochastic neural networks (SNNs) with Markovian jump parameters, mixed time delays, andα-inverse Hölder activation functions is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Firstly, based on Brouwer degree properties, the existence and uniqueness of the equilibrium point for SNNs without noise perturbations are proved. Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI) technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. Finally, two simulation examples are provided to demonstrate the validity of the theoretical results.

scholarly journals Exponential Synchronization for Stochastic Neural Networks with Mixed Time Delays and Markovian Jump Parameters via Sampled Data

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yingwei Li ◽  
Xueqing Guo
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Stochastic Neural Networks ◽  
Sampled Data ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays ◽  
Data Controller

The exponential synchronization issue for stochastic neural networks (SNNs) with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI) approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Novel Robust Exponential Stability of Markovian Jumping Impulsive Delayed Neural Networks of Neutral-Type with Stochastic Perturbation

2016 ◽  
Vol 2016 ◽  
pp. 1-20
Author(s):  
Yang Fang ◽  
Kelin Li ◽  
Yunqi Yan
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Neutral Type ◽  
Stochastic Perturbation ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Delayed Neural Networks

The robust exponential stability problem for a class of uncertain impulsive stochastic neural networks of neutral-type with Markovian parameters and mixed time-varying delays is investigated. By constructing a proper exponential-type Lyapunov-Krasovskii functional and employing Jensen integral inequality, free-weight matrix method, some novel delay-dependent stability criteria that ensure the robust exponential stability in mean square of the trivial solution of the considered networks are established in the form of linear matrix inequalities (LMIs). The proposed results do not require the derivatives of discrete and distributed time-varying delays to be 0 or smaller than 1. Moreover, the main contribution of the proposed approach compared with related methods lies in the use of three types of impulses. Finally, two numerical examples are worked out to verify the effectiveness and less conservativeness of our theoretical results over existing literature.

scholarly journals Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Iswarya Manickam ◽  
Raja Ramachandran ◽  
Grienggrai Rajchakit ◽  
Jinde Cao ◽  
Chuangxia Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Theoretic Approach ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Markovian Jump Parameters ◽  
Graph Theoretic ◽  
Mixed Time Delays ◽  
Graph Theoretic Approach

This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.

scholarly journals Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Quanxin Zhu ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Stochastic Stability ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computationally Efficient ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Finite State ◽  
Theoretical Results

The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given in the previous literature.

On exponential stability of delayed neural networks with a general class of activation functions

2002 ◽  
Vol 298 (2-3) ◽  
pp. 122-132 ◽  
Author(s):  
Changyin Sun ◽  
Kanjian Zhang ◽  
Shumin Fei ◽  
Chun-Bo Feng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
General Class ◽  
Activation Functions ◽  
Delayed Neural Networks
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