scholarly journals Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 101 ◽  
Author(s):  
Jinlong Shu ◽  
Lianglin Xiong ◽  
Tao Wu ◽  
Zixin Liu
Keyword(s):  
Neural Networks ◽  
Convex Combination ◽  
Neutral Type ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Inequality Technique ◽  
Combination Approach ◽  
Complex Valued

This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.

Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

2021 ◽  
Vol 8 (3) ◽  
pp. 486-498
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
State Feedback ◽  
Neutral Type ◽  
State Feedback Control ◽  
Projective Synchronization ◽  
Time Varying ◽  
Master System ◽  
Complex Valued ◽  
Theoretical Results

This paper deals with the problem of finite-time projective synchronization for a class of neutral-type complex-valued neural networks (CVNNs) with time-varying delays. A simple state feedback control protocol is developed such that slave CVNNs can be projective synchronized with the master system in finite time. By employing inequalities technique and designing new Lyapunov--Krasovskii functionals, various novel and easily verifiable conditions are obtained to ensure the finite-time projective synchronization. It is found that the settling time can be explicitly calculated for the neutral-type CVNNs. Finally, two numerical simulation results are demonstrated to validate the theoretical results of this paper.

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 STABILITY CRITERIA ON DISCRETE-TIME NEURAL NETWORKS WITH BOTH TIME-VARYING AND DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (04) ◽  
pp. 269-283 ◽  
Author(s):  
TAO LI ◽  
AIGUO SONG ◽  
SHUMIN FEI
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Combination Methods

This paper investigates robust exponential stability for discrete-time recurrent neural networks with both time-varying delay (0 ≤ τm ≤ τ(k) ≤ τM) and distributed one. Through partitioning delay intervals [0,τm] and [τm,τM], respectively, and choosing an augmented Lyapunov-Krasovskii functional, the delay-dependent sufficient conditions are obtained by using free-weighting matrix and convex combination methods. These criteria are presented in terms of linear matrix inequalities (LMIs) and their feasibility can be easily checked by resorting to LMI in Matlab Toolbox in Ref. 1. The activation functions are not required to be differentiable or strictly monotonic, which generalizes those earlier forms. As an extension, we further consider the robust stability of discrete-time delayed Cohen-Grossberg neural networks. Finally, the effectiveness of the proposed results is further illustrated by three numerical examples in comparison with the reported ones.

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