scholarly journals LMI Approach to Stability Analysis of Cohen-Grossberg Neural Networks withp-Laplace Diffusion

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Exponentially Stable ◽  
New Criterion ◽  
Diffusion Simulation ◽  
And Diffusion ◽  
Laplace Diffusion

The nonlinearp-Laplace diffusion (p>1) was considered in the Cohen-Grossberg neural network (CGNN), and a new linear matrix inequalities (LMI) criterion is obtained, which ensures the equilibrium of CGNN is stochastically exponentially stable. Note that, ifp=2,p-Laplace diffusion is just the conventional Laplace diffusion in many previous literatures. And it is worth mentioning that even ifp=2, the new criterion improves some recent ones due to computational efficiency. In addition, the resulting criterion has advantages over some previous ones in that both the impulsive assumption and diffusion simulation are more natural than those of some recent literatures.

AUTOASSOCIATIVE MEMORY DESIGN USING INTERCONNECTED GENERALIZED BRAIN-STATE-IN-A-BOX NEURAL NETWORKS

2005 ◽  
Vol 15 (03) ◽  
pp. 181-196 ◽  
Author(s):  
CHEOLHWAN OH ◽  
STANISLAW H. ŻAK ◽  
GUISHENG ZHAI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Brain State ◽  
Stability Conditions ◽  
Network Architectures ◽  
Associative Memories ◽  
Matrix Inequalities ◽  
Memory Design

A class of interconnected neural networks composed of generalized Brain-State-in-a-Box (gBSB) neural subnetworks is considered. Interconnected gBSB neural network architectures are proposed along with their stability conditions. The design of the interconnected neural networks is reduced to the problem of solving linear matrix inequalities (LMIs) to determine the interconnection parameters. A method for solving LMIs is devised generating the solutions that, in general, are further away from zero than the corresponding solutions obtained using MATLAB's LMI toolbox, thus resulting in stronger interconnections between the subnetworks. The proposed architectures are then used to construct neural associative memories. Simulations are performed to illustrate the results obtained.

scholarly journals Synchronization of Switched Complex Bipartite Neural Networks with Infinite Distributed Delays and Derivative Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Qiuxiang Bian ◽  
Jinde Cao ◽  
Jie Wu ◽  
Hongxing Yao ◽  
Tingfang Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Derivative Coupling ◽  
Infinite Distributed Delays ◽  
Theoretical Results

A new model of switched complex bipartite neural network (SCBNN) with infinite distributed delays and derivative coupling is established. Using linear matrix inequality (LMI) approach, some synchronization criteria are proposed to ensure the synchronization between two SCBNNs by constructing effective controllers. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results obtained in this paper.

scholarly journals Improved Results onH∞State Estimation of Static Neural Networks with Time Delay

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Bin Wen ◽  
Hui Li ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Estimator ◽  
Static Neural Networks ◽  
Exponentially Stable ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

This paper studies the problem ofH∞state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribedH∞performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

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.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

Monotonic Convergence Analysis for 2-D Roesser Systems via a LMI Approach

2014 ◽  
Vol 575 ◽  
pp. 594-597
Author(s):  
Zhi Fu Li ◽  
Yue Ming Hu
Keyword(s):  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Dimensional System ◽  
Matrix Inequalities ◽  
Roesser Model ◽  
Lmi Approach ◽  
One Dimensional ◽  
Bibo Stability ◽  
Monotonic Convergence ◽  
Bounded Input

The monotonic convergence (MC) property of discrete two-dimensional (2-D) systems described by the Roesser model is studied. The MC problem of the 2-D system is firstly converted to two H∞ disturbance attenuation problems of the traditional one-dimensional system. Then, the sufficient condition is derived for the MC, which is given by two linear matrix inequalities (LMIs). Furthermore, it can be shown that either of the LMIs can also guarantee the Bounded-Input Bounded-Output (BIBO) stability of the 2-D system. Finally, a simulation example is given to show the effectiveness of the LMIs condition.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

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