Global μ-stability of complex-valued delayed neural networks with leakage delay

Dissipativity and passivity analysis for discrete-time T–S fuzzy stochastic neural networks with leakage time-varying delays based on Abel lemma approach

“…However, several techniques such as free weighting matrix method [7], Jensen's inequality [5], Wirtinger's inequality [10] are available to deal with time-varying delay τ (k) for obtaining less conservative result. Different from these approaches, Abel lemma based finite-sum inequality would be more computational efficient, since no slack variables are introduced for computation which can be seen through numerical examples.…”

“…Furthermore, neural networks with leakage delay is a class of important neural networks as time delay in the leakage term has great impact on the dynamics of neural networks since time delay in the stabilizing negative feedback term has a tendency to destabilize a system. Recently, in [1], the authors investigated stability analysis for discrete-time neural networks with leakage time-varying delays by using reciprocally convex combination approach whereas stability of complex valued delayed neural networks with leakage delay is addressed in [5].…”

Finite time anti-synchronization of complex-valued neural networks with bounded asynchronous time-varying delays

“…Besides, it is natural to deduce CVNNs to more complicated quaternion-valued neural networks (QVNNs). Therefore, many scholars are attracted to study the dynamical behaviors and properties of CVNNs, see [11], [22]- [27], [29,30,33]. Synchronization (SYN), which is a special case of dynamical behaviors, has been extensively studied in the recent past because of its significant role in combinatorial optimization, image processing, secure communication [6] and many other fields since it was proposed by Pecora and Carroll [7].…”

“…One common technique is to decompose the complex-valued activation functions to its real and imaginary parts, as a result, the original CVNNs are separated into double RVNNs, many results have been obtained by applying this method, see [22]- [30]. In [24,27], the authors investigate the µ-stability of CVNNs with unbounded time-varying delays when f (z) can be expressed [26] considers the exponential stability problem for CVNN with time-varying delays, sufficient criteria are obtained based on the matrix measure method and Halanay inequality method, and in [28], the exponential SYN and A-SYN problems of complex-valued MNN with bounded delays are also solved with these two mathematical tools. [29] investigates the exponential stability for CVNNs with asynchronous time delays by decomposing and recasting an equivalent RVNN, some sufficient conditions are given under three generalized norms.…”

“…-(27) are: µ 1 > 14.675, µ 1 > 11.9, µ 2 > 7.531, µ 2 > 10.008,ρ 1 > (12.681 − µ 1 ) + = 0, ρ 1 > (8.244 − µ 1 ) + = 0, ρ 2 > (2.665 − µ 2 ) + = 0, ρ 2 > (4.393 − µ 2 ) + = 0,η 1 ≥ 5, η 1 ≥ 5, η 2 ≥ 6.6, η 2 ≥ 6.6…”