Improvement on reciprocally convex combination lemma and quadratic function negative-definiteness lemma

2021 ◽  
Author(s):  
Jun Chen ◽  
Ju H. Park ◽  
Shengyuan Xu
Keyword(s):  
Convex Combination ◽  
Quadratic Function ◽  
Reciprocally Convex Combination

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 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.

scholarly journals Further Results on Stability Analysis for Uncertain Delayed Neural Networks with Reliable Memory Feedback Control

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Wenhao Wang ◽  
Xiao Cai ◽  
Kaibo Shi ◽  
Hong Zhu ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Feedback Control ◽  
Convex Combination ◽  
Quadratic Function ◽  
System Stability ◽  
Combination Method ◽  
Delayed Neural Networks ◽  
Theoretical Results

This study proposes further results for the stability analysis issue of uncertain delayed neural networks (UDNNs) via the reliable memory feedback control scheme. First, an improved quadratic function method is introduced for constructing a novel term V 1 x t , which can fully excavate some intrinsic relationships between the delay derivative information and time-delay information. Based on the time-delay-product function (TDPF) and linear convex combination method (LCCM), the information storage is further improved for obtaining new theoretical results. Second, by using resultful integral inequalities and correlation analysis approaches, several relaxed criteria are established with respect to the asymptotical stability of the considered UDNNs. Third, the desired reliable memory feedback controller (RMFC) is achieved, which can ensure the system stability of UDNNs. Lastly, two numerical experiments are given to illustrate the significance of the theoretical 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.

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