Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays

2011 ◽  
Vol 41 (2) ◽  
pp. 341-353 ◽  
Author(s):  
Quanxin Zhu ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Delays ◽  
Stochastic Neural Networks ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays

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 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.

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