scholarly journals Stability Analysis for Delayed Neural Networks: Reciprocally Convex Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hongjun Yu ◽  
Xiaozhan Yang ◽  
Chunfeng Wu ◽  
Qingshuang Zeng
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Convex Combination ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Combination Approach ◽  
Continuous Neural Networks ◽  
Delay Dependent

This paper is concerned with global stability analysis for a class of continuous neural networks with time-varying delay. The lower and upper bounds of the delay and the upper bound of its first derivative are assumed to be known. By introducing a novel Lyapunov-Krasovskii functional, some delay-dependent stability criteria are derived in terms of linear matrix inequality, which guarantee the considered neural networks to be globally stable. When estimating the derivative of the LKF, instead of applying Jensen’s inequality directly, a substep is taken, and a slack variable is introduced by reciprocally convex combination approach, and as a result, conservatism reduction is proved to be more obvious than the available literature. Numerical examples are given to demonstrate the effectiveness and merits of the proposed method.

scholarly journals Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten Stojanovic ◽  
Milan Stojanovic ◽  
Milos Stevanovic
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

Improved Results on Finite-Time Stability Analysis of Neural Networks With Time-Varying Delays

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. Saravanan ◽  
M. Syed Ali
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Finite Time ◽  
Lyapunov Functional ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Finite Time Stability ◽  
Combination Methods

This paper investigates the issue of finite time stability analysis of time-delayed neural networks by introducing a new Lyapunov functional which uses the information on the delay sufficiently and an augmented Lyapunov functional which contains some triple integral terms. Some improved delay-dependent stability criteria are derived using Jensen's inequality, reciprocally convex combination methods. Then, the finite-time stability conditions are solved by the linear matrix inequalities (LMIs). Numerical examples are finally presented to verify the effectiveness of the obtained results.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method. Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach. Moreover, our criteria depend on both the upper and lower bounds on time-varying delay and its derivative, which is different from some existing ones. Finally, a numerical example is given to show the improved stability region of the proposed results.

Improved Stability Analysis for Neural Networks with Interval Time-Varying Delays

2014 ◽  
Vol 687-691 ◽  
pp. 2078-2082 ◽  
Author(s):  
Ze Rong Ren ◽  
Jun Kang Tian
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered. By the use of delay-partitioning method and some novel techniques, some less conservative stability criteria are established in terms of linear matrix inequalities. Moreover, our criteria depend on both the upper and lower bounds of time-varying delay and its derivative, which is different from some existing ones. Finally, an numerical example is given to show the improved stability region of the proposed results.

scholarly journals Stability Analysis of Systems with Interval Time-Varying Delays via a New Integral Inequality

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zerong Ren ◽  
Jun-kang Tian
Keyword(s):  
Stability Analysis ◽  
Integral Inequality ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Interval Time ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper focuses on delay-dependent stability analysis for systems with interval time-varying delays. Based on a new integral inequality and a generalized reciprocally convex combination matrix inequality, a new delay-dependent stability criterion is obtained in terms of a linear matrix inequality (LMI). Finally, the merits of the proposed criterion are shown by two numerical examples.

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 Robust State Estimation for Delayed Neural Networks with Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Delayed Neural Networks ◽  
Stochastic Parameter ◽  
Mean And Variance ◽  
Delay Dependent ◽  
Designing Method ◽  
Dependent State

This paper considers the problem of delay-dependent state estimation for neural networks with time-varying delays and stochastic parameter uncertainties. It is assumed that the parameter uncertainties are affected by the environment which is changed with randomly real situation, and its stochastic information such as mean and variance is utilized in the proposed method. By constructing a newly augmented Lyapunov-Krasovskii functional, a designing method of estimator for neural networks is introduced with the framework of linear matrix inequalities (LMIs) and a neural networks model with stochastic parameter uncertainties which have not been introduced yet. Two numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed idea.

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