Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality

Abstract

SummaryThis paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval time‐varying delays. Different from previous literature, some sufficient information on a complex‐valued neuron activation function and interval time‐varying delays has been considered into the record. A suitable Lyapunov‐Krasovskii functional with some delay‐dependent terms is constructed. By applying modern integral inequalities, several sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed system model. All the proposed criteria are formulated in the structure of a complex‐valued linear matrix inequalities technique, which can be checked effortlessly by applying the YALMIP toolbox in MATLAB linear matrix inequality. Finally, two numerical examples with simulation results have been provided to demonstrate the efficiency of the proposed method.

Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties

“…Remark 1. From the inequalities (8) and (9), it is confirmed that (I − J F (t)) is invertible. Given J = 0, the following norm-bounded parametric uncertainty form ∆ T (t)∆(t) = F T (t)F (t) ≤ I can be obtained from the linear fractional uncertainty of the form (6).…”

“…). Suppose ∆(t) is given by (6)- (8). Given M and N are of appropriate dimensions and matrix Ξ = Ξ T the inequality…”

“…Remark 5. In recent years, dynamical analysis with respect to various CVNN models has been conducted [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][31][32][33][34][35][36][37]. In this regard, the research interest pertaining to HTCVNN models has increased significantly in recent years [1,13,[16][17][18].…”

Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

“…On the other hand, stability is a key requirement for a system to function properly and safely. As such, it is important to carry out the stability analysis of NNs, and they have received considerable attention [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…In addition, CVNN consists of complex-valued states, inputs, connection weights, and activation functions. As a result, the investigation of CVNNs has increased [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”