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.

New results on robust passivity analysis of neural networks with interval nondifferentiable and distributed time-varying delays are investigated. It is assumed that the parameter uncertainties are norm-bounded. By construction an appropriate Lyapunov-Krasovskii containing single, double, triple and quadruple integrals, which fully utilize information of the neuron activation function and use refined Jensen's inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.

This paper is concerned with the dissipative problem based pinning sampled-data control scheme. We investigate the problem for function projective synchronization of neural networks with hybrid couplings and time-varying delays. The main purpose is focused on designing a pinning sampled-data function projective synchronization controller such that the resulting function projective synchronization neural networks are stable and satisfy a strictly H∞,L2 - L∞, passivity and dissipativity performance by setting parameters in the general performance index. It is assumed that the parameter uncertainties are norm-bounded. By construction of an appropriate Lyapunov-Krasovskii containing single, double and triple integrals, which fully utilize information of the neuron activation function and use refined Jensen’s inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.

This study explores the challenge of achieving consensus in multi-agent systems (MASs) when facing the random packet dropouts and disturbances. It employs memory state-feedback control (MSFC) in the context of undirected graphs and specified leader agents. The analysis focuses on mean square consensus, considering MASs within strongly connected networks or networks with undirected spanning trees. The MSFC approach is developed to ensure asymptotic consensus despite packet dropouts and also to reduce the impact of disturbances. Specifically, the consensus analysis leverages the Lyapunov-Krasovskii functional (LKF) framework, and the necessary conditions for implementing the proposed MSFC are established using linear matrix inequalities (LMIs). The system, augmented with an \(H_{\infty}\) attenuation level, is guaranteed to achieve asymptotic mean-square stability according to the provided criteria. In conclusion, two examples are provided to illustrate the effectiveness and practicality of the proposed control mechanism.

This paper presents the problem of mixed H ∞ $H_{\infty }$ /passive exponential function projective synchronization of delayed neural networks with constant discrete and distributed delay couplings under pinning sampled-data control scheme. The aim of this work is to focus on designing of pinning sampled-data controller with an explicit expression by which the stable synchronization error system is achieved and a mixed H ∞ $H_{\infty }$ /passive performance level is also reached. Particularly, the control method is designed to determine a set of pinned nodes with fixed coupling matrices and strength values, and to select randomly pinning nodes. To handle the Lyapunov functional, we apply some new techniques and then derive some sufficient conditions for the desired controller existence. Furthermore, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.