This article investigates the security consensus problem for fractional-order multiagent systems (FOMASs) with cyber attacks via the hybrid event-triggered and impulsive control strategy. First, based on the destructive characteristics of network attacks on communication channels, a method for separating partial network structures is proposed. Differing from other studies of multiagent systems, it considers here that the communication topological network consists of strong channel and weak channel networks, and its connectivity is not required. Then, to overcome bandwidth constraints, a new hybrid event-triggered and impulsive security consensus control approach is first designed, which only needs to detect the sampled data at instants of cyber attacks and impulse. Furthermore, applying the fractional Lyapunov stability analysis methods, several sufficient conditions are proposed to achieve the exponential consensus for FOMASs with cyber attacks. Meanwhile, some parameters in security consensus control protocol are acquired. Finally, from the perspective of numerical simulation visualization, the rationality and correctness of the proposed consensus security control method are verified.

This paper addresses the state-dependent impulsive effects on robust exponential stability of quaternion-valued neural networks (QVNNs) with parametric uncertainties. In view of the noncommutativity of quaternion multiplication, we have to separate the concerned quaternion-valued models into four real-valued parts. Then, several assumptions ensuring every solution of the separated state-dependent impulsive neural networks intersects each of the discontinuous surface exactly once are proposed. In the meantime, by applying the B -equivalent method, the addressed state-dependent impulsive models are reduced to fixed-time ones, and the latter can be regarded as the comparative systems of the former. For the subsequent analysis, we proposed a novel norm inequality of block matrix, which can be utilized to analyze the same stability properties of the separated state-dependent impulsive models and the reduced ones efficaciously. Afterward, several sufficient conditions are well presented to guarantee the robust exponential stability of the origin of the considered models; it is worth mentioning that two cases of addressed models are analyzed concretely, that is, models with exponential stable continuous subsystems and destabilizing impulses, and models with unstable continuous subsystems and stabilizing impulses. In addition, an application case corresponding to the stability problem of models with unstable continuous subsystems and stabilizing impulses for state-dependent impulse control to robust exponential synchronization of QVNNs is considered summarily. Finally, some numerical examples are proffered to illustrate the effectiveness and correctness of the obtained results.

This paper addresses the issue of state estimation for the quaternion-valued neural networks (QVNNs) with leakage, discrete, and distributed delays by employing the Lyapunov stability theory and the quaternion matrix theory. The criteria are developed in two forms of quaternion-valued linear matrix inequalities (LMIs) and complex-valued LMIs for guaranteeing the existence and stability of state estimators of the delayed QVNNs. Two numerical examples are provided to illustrate the effectiveness of the obtained results.

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

This paper addresses the multistability issue for quaternion-valued neural networks (QVNNs) with time delays. By using the inequality technique, sufficient conditions are proposed for the boundedness and the global attractivity of delayed QVNNs. Based on the geometrical properties of the activation functions, several criteria are obtained to ensure the existence of equilibrium points, of which are locally stable. Two numerical examples are provided to illustrate the effectiveness of the obtained results.

This paper addresses the problem of designing associative memories based on quaternion-valued neural networks (QVNNs). A system designing procedure for QVNNs is developed by employing quaternion matrix decomposition, and a given set of states can be assigned as the equilibrium points of the designed QVNNs. Moreover, some sufficient conditions for the asymptotic stability of the equilibrium points are obtained via Lyapunov's direct method. Numerical simulations manifest that the constructed QVNNs work efficiently on storing and retrieving blurred gray-scale and true color images.

In this paper, the boundedness and complete stability of complex-valued neural networks (CVNNs) with time delay are studied. Some conditions to guarantee the boundedness of the CVNNs are derived using local inhibition. Moreover, under the boundedness conditions, a compact set that globally attracts all the trajectories of the network is also given. Additionally, several conditions in terms of real-valued linear matrix inequalities (LMIs) for complete stability of the CVNNs are established via the energy minimization method and the approach that converts the complex-valued LMIs to real-valued ones. Examples with simulation results are given to show the effectiveness of the theoretical analysis.

In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.

In this correspondence, the impulsive effects on the stability of fuzzy Cohen-Grossberg neural networks (FCGNNs) with time-varying delays are considered. Several sufficient conditions are obtained ensuring global exponential stability of equilibrium point for the neural networks by the idea of vector Lyapunov function, M-matrix theory, and analytic methods. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results not only show that the stability still remains under certain impulsive perturbations for the continuous stable FCGNNs with time-varying delays, but also present an approach to stabilize the unstable FCGNNs with time-varying delays by utilizing impulsive effects. An example with simulations is given to show the effectiveness of the obtained results.