New Delay-Dependent Stability Criteria for Recurrent Neural Networks with Time-Varying Delays

2014 ◽  
Vol 513-517 ◽  
pp. 922-926
Author(s):  
Ze Rong Ren ◽  
Xiang Jun Xie
Keyword(s):  
Neural Networks ◽  
Stability Criterion ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Neuron Activation ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Delay Dependent Stability

This paper is concerned with the problem of delay-dependent asymptotic stability criterion for recurrent neural networks with time-varying delays. A new Lyapunov functional is introduced by considering the information of neuron activation functions adequately. By using the improved delay-partitioning method and reciprocally convex approach, a less conservative stability criterion is obtained in terms of linear matrix inequalities (LMIs). A numerical example is finally given to illustrate the effectiveness of the derived method.

scholarly journals Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
New Inequalities

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

Stability analysis for discrete-time neural networks with time-varying delays and stochastic parameter uncertainties

2015 ◽  
Vol 93 (4) ◽  
pp. 398-408 ◽  
Author(s):  
O.M. Kwon ◽  
M.J. Park ◽  
S.M. Lee ◽  
E.J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Stochastic Parameter ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper proposes new delay-dependent stability criteria for discrete-time neural networks with interval time-varying delays and probabilistic occurring parameter uncertainties. It is assumed that parameter uncertainties are changed with the environment, explored using random situations, and its stochastic information is included in the proposed method. By constructing a suitable Lyapunov–Krasovskii functional, new delay-dependent stability criteria for the concerned systems are established in terms of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Improved Results on Robust Stability for Systems with Interval Time-Varying Delays and Nonlinear Perturbations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xin Zhou ◽  
Hexin Zhang ◽  
Xiaoxiang Hu ◽  
Junjun Hui ◽  
Tianmei Li
Keyword(s):  
Robust Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Delay Dependent Stability

This paper investigated delay-dependent robust stability criteria for systems with interval time-varying delays and nonlinear perturbations. A delay-partitioning approach is used in this paper, the delay-interval is partitioned into multiple equidistant subintervals, a new Lyapunov-Krasovskii (L-K) functional contains some triple-integral terms, and augment terms are introduced on these intervals. Then, by using integral inequalities method together with free-weighting matrix approach, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Delay-Dependent Asymptotical Stabilization Criterion of Recurrent Neural Networks

2013 ◽  
Vol 330 ◽  
pp. 1045-1048 ◽  
Author(s):  
Grienggrai Rajchakit
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Lyapunov Functional ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the problem of delay-dependent stability criterion of discrete-time recurrent neural networks with time-varying delays. Based on quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criteria are found to guarantee delay-dependent asymptotical stability of these systems. And one example illustrates the exactness of the proposed criteria.

scholarly journals Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Delay-Dependent Stability Criteria of Uncertain Periodic Switched Recurrent Neural Networks with Time-Varying Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Xing Yin ◽  
Jun Li ◽  
Weigen Wu ◽  
Qiranrong Tan
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Switching State

This paper deals with the problem of delay-dependent stability criterion of uncertain periodic switched recurrent neural networks with time-varying delays. When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach (SQLF) and free-weighting matrix approach (FWM), some linear matrix inequality criteria are found to guarantee the delay-dependent asymptotical stability of these systems. Two examples illustrate the exactness of the proposed criteria.

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