scholarly journals Synchronization of Fractional Order Uncertain BAM Competitive Neural Networks

2021 ◽  
Vol 6 (1) ◽  
pp. 14
Author(s):  
M. Syed Ali ◽  
M. Hymavathi ◽  
Syeda Asma Kauser ◽  
Grienggrai Rajchakit ◽  
Porpattama Hammachukiattikul ◽  
...  
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Bidirectional Associative Memory ◽  
Numerical Examples ◽  
Novel Approach ◽  
Theoretical Results

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.

Dynamical analysis of memristor-based fractional-order neural networks with time delay

2016 ◽  
Vol 30 (18) ◽  
pp. 1650271 ◽  
Author(s):  
Xueli Cui ◽  
Yongguang Yu ◽  
Hu Wang ◽  
Wei Hu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Time Varying ◽  
Numerical Examples

In this paper, the memristor-based fractional-order neural networks with time delay are analyzed. Based on the theories of set-value maps, differential inclusions and Filippov’s solution, some sufficient conditions for asymptotic stability of this neural network model are obtained when the external inputs are constants. Besides, uniform stability condition is derived when the external inputs are time-varying, and its attractive interval is estimated. Finally, numerical examples are given to verify our results.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

scholarly journals Passivity of Memristive BAM Neural Networks with Probabilistic and Mixed Time-Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-25
Author(s):  
Weiping Wang ◽  
Meiqi Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Wenbing Zhao
Keyword(s):  
Neural Networks ◽  
Probability Distribution ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Bernoulli Distribution ◽  
Matrix Inequalities ◽  
Bidirectional Associative Memory ◽  
Leakage Delays ◽  
Numerical Examples

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

scholarly journals Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 422 ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Pharunyou Chanthorn ◽  
Pramet Kaewmesri ◽  
Ramalingam Sriraman ◽  
Chee Peng Lim
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
State Feedback ◽  
Control Law ◽  
Memristive Neural Networks ◽  
Numerical Examples ◽  
Quaternion Multiplication ◽  
Stabilizing Control ◽  
Stability And Stabilization

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

scholarly journals New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ahmed Alsaedi ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Delayed Neural Networks ◽  
New Methods ◽  
Theoretical Results

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results.

Global stabilization of memristor-based fractional-order neural networks with delay via output-feedback control

2017 ◽  
Vol 31 (05) ◽  
pp. 1750031 ◽  
Author(s):  
Jiyang Chen ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Xujun Yang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Output Feedback ◽  
Differential Inclusions ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Global Stabilization ◽  
Lyapunov Direct Method ◽  
Stabilizing Control

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.

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.

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