Dissipativity analysis of time-delayed neural networks using a vector-related zero-value-term method and generalized reciprocally convex combination techniques

2020 ◽  
Author(s):  
WANG Chen-Rui ◽  
HE Yong
Keyword(s):  
Neural Networks ◽  
Convex Combination ◽  
Delayed Neural Networks ◽  
Reciprocally Convex Combination ◽  
Dissipativity Analysis

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.

Novel results on dissipativity analysis for generalized delayed neural networks

2019 ◽  
Vol 332 ◽  
pp. 328-338 ◽  
Author(s):  
Can Zhao ◽  
Shouming Zhong ◽  
Xiaojun Zhang ◽  
Kaibo Shi
Keyword(s):  
Neural Networks ◽  
Delayed Neural Networks ◽  
Dissipativity Analysis

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 LMI-Based Results on Robust Exponential Passivity of Uncertain Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays via the Reciprocally Convex Combination Technique

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 70
Author(s):  
Nayika Samorn ◽  
Narongsak Yotha ◽  
Pantiwa Srisilp ◽  
Kanit Mukdasai
Keyword(s):  
Neural Networks ◽  
Model Transformation ◽  
Convex Combination ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Combination Technique ◽  
Reciprocally Convex Combination

The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, the lower bounds of the delays are allowed to be either positive or zero adopting the combination of the model transformation, various inequalities, the reciprocally convex combination, and suitable Lyapunov–Krasovskii functional. A new robust exponential passivity criterion is received and formulated in the form of linear matrix inequalities (LMIs). Moreover, a new exponential passivity criterion is also examined for systems without uncertainty. Four numerical examples indicate our potential results exceed the previous results.

scholarly journals Stochastically exponential synchronization for Markov jump neural networks with time-varying delays via event-triggered control scheme

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaoman Liu ◽  
Haiyang Zhang ◽  
Jun Yang ◽  
Hao Chen
Keyword(s):  
Neural Networks ◽  
Convex Combination ◽  
Analytical Techniques ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Markov Jump ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Reciprocally Convex Combination ◽  
Event Triggered

AbstractThis paper focuses on the stochastically exponential synchronization problem for one class of neural networks with time-varying delays (TDs) and Markov jump parameters (MJPs). To derive a tighter bound of reciprocally convex quadratic terms, we provide an improved reciprocally convex combination inequality (RCCI), which includes some existing ones as its particular cases. We construct an eligible stochastic Lyapunov–Krasovskii functional to capture more information about TDs, triggering signals, and MJPs. Based on a well-designed event-triggered control scheme, we derive several novel stability criteria for the underlying systems by employing the new RCCI and other analytical techniques. Finally, we present two numerical examples to show the validity of our methods.

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.

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