scholarly journals Global Asymptotic Stability of Switched Neural Networks with Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Zhenyu Lu ◽  
Kai Li ◽  
Yan Li
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Global Asymptotic Stability ◽  
Recent Literature ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Numerical Example ◽  
Switched Neural Networks ◽  
New Criteria

This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs) are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.

scholarly journals New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Global Asymptotic Stability ◽  
Positive Definite ◽  
Time Varying ◽  
Numerical Example ◽  
Definite Form ◽  
Takagi Sugeno

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods.

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.

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.

Improvement of Admissibility of Linear Singular Fractional Order Systems

2019 ◽  
Author(s):  
XueFeng Zhang ◽  
Yingbo Zhang
Keyword(s):  
Fractional Order ◽  
Linear Matrix Inequalities ◽  
Equality Constraint ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Strict Lmis ◽  
New Criteria

Abstract This paper considers the least solutions of linear matrix inequalities (LMIs) in criteria of admissibility for continuous singular fractional order systems (FOS). The new criteria are given which are strict LMIs and do not involve equality constraint and with the less LMI decision variables. With brief and simple results of this paper, the numbers of solved matrices are reduced from a pair of matrices to just a matrix in which we can analyze singular fractional order systems with completely consistent format as normal systems.

Synchronization of delayed neural networks with hybrid coupling via impulsive control

2019 ◽  
Vol 41 (13) ◽  
pp. 3714-3724 ◽  
Author(s):  
Tianhu Yu ◽  
Huamin Wang ◽  
Dengqing Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Upper Bound ◽  
Hybrid Control ◽  
Impulsive Control ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Delayed Neural Networks ◽  
Coupled Neural Networks

The synchronization problem of coupled neural networks via impulsive control is investigated in the present paper. Based on a time varying Lyapunov functional associated with the impulsive time sequence, the delay-dependent criteria in terms of linear matrix inequalities are derived to guarantee the synchronization of the coupled neural networks. The obtained criteria are closely related to both the lower and the upper bound of the adjacent impulsive instant difference. By solving the corresponding linear matrix inequalities, the synchronization criteria can be used to estimate the upper bound of both transmission delay and distributed-delay. The low-dimensional criteria also are obtained for the coupled neural networks with identical nodes. Finally, two examples are given to illustrate the validity of the proposed hybrid control.

Stability Analyses of Neural Networks with Unbounded Time-Varying Delays and Nonlinear Perturbations

2013 ◽  
Vol 278-280 ◽  
pp. 1247-1250 ◽  
Author(s):  
Li Zi Yin
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Functional Method ◽  
Neural Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Stability Analyses

In this paper, we consider the problem of mu-stability of unbounded time-varying delays neural systems with nonlinear perturbations. Some mu-stability criterias are derived by using Lyapunov- Krasovski functional method . Those criteria are expressed in the form of linear matrix inequalities (LMIs).

LMI-BASED ASYMPTOTIC STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (03) ◽  
pp. 257-265 ◽  
Author(s):  
TAO LI ◽  
CHANGYIN SUN ◽  
XIANLIN ZHAO ◽  
CHONG LIN
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Activation Functions ◽  
Different Types ◽  
Conservative Result

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

scholarly journals New Results on Passivity for Discrete-Time Stochastic Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei Kang ◽  
Jun Cheng ◽  
Xiangyang Cheng
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for discrete-time stochastic neural networks with time-varying delays is investigated in this paper. New delay-dependent passivity conditions are obtained in terms of linear matrix inequalities. Less conservative conditions are obtained by using integral inequalities to aid in the achievement of criteria ensuring the positiveness of the Lyapunov-Krasovskii functional. At last, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals On the stability of 2D general Roesser Lyapunov systems

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 85-97
Author(s):  
Mohammed Amine Ghezzar ◽  
Djillali Bouagada ◽  
Kamel Benyettou ◽  
Mohammed Chadli ◽  
Paul Van Dooren
Keyword(s):  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
The Stability

This paper addresses the problem of stability for general two-dimensional (2D) discrete-time and continuous-discrete time Lyapunov systems, where the linear matrix inequalities (LMI's) approach is applied to derive a new sufficient condition for the asymptotic stability.

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