scholarly journals LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Ruofeng Rao ◽  
Xiongrui Wang ◽  
Shouming Zhong ◽  
Zhilin Pu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Schur Complement ◽  
Great Difficulty ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Almost Sure Exponential Stability ◽  
The Stability ◽  
Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

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 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.

scholarly journals Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chunge Lu ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

This paper investigates mean-square robust exponential stability of the equilibrium point of stochastic neural networks with leakage time-varying delays and impulsive perturbations. By using Lyapunov functions and Razumikhin techniques, some easy-to-test criteria of the stability are derived. Two examples are provided to illustrate the efficiency of the results.

ALMOST SURE EXPONENTIAL STABILITY OF STOCHASTIC RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2010 ◽  
Vol 20 (02) ◽  
pp. 539-544 ◽  
Author(s):  
LI WAN ◽  
QINGHUA ZHOU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Almost Sure Exponential Stability ◽  
The Stability

The stability of stochastic recurrent neural networks with time-varying delays is investigated. A set of novel sufficient conditions on almost sure exponential stability has been established. Two examples are also given to illustrate the effectiveness of our results.

ROBUST EXPONENTIAL STABILITY OF MARKOVIAN JUMPING NEURAL NETWORKS WITH TIME-VARYING DELAY

2008 ◽  
Vol 18 (03) ◽  
pp. 207-218 ◽  
Author(s):  
MING GAO ◽  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Condition ◽  
Time Varying ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the robust stability of a class of neural networks with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov–Krasovskii functional, a sufficient condition for the global exponential stability of the delayed Markovian jumping neural networks is established. The proposed condition is also extended to the uncertain cases, which are shown to be the improvement and extension of the existing ones. Finally, the validity of the results are illustrated by an example.

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