Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach

In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme

Exponential synchronization for second-order switched quaternion-valued neural networks with neutral-type and mixed time-varying delays

This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes

Existence and exponential stability of solutions for quaternion-valued delayed hopfield neural networks by ξ-Norms

© 2013 IEEE. Recently, with the development of quaternion applications, quaternion-valued neural networks (QVNNs) have been presented and studied by more and more scholars. In this paper, the existence, uniqueness and exponential stability criteria of solutions for the quaternion-valued delayed Hopfield neural networks (QVDHNNs) are mainly investigated by means of the definitions of ξ-norms. In order to construct a ξ-norm, QVDHNNs system are decomposed into four real-number systems according to Hamilton rules. Then, taking advantage of ξ-norms, inequality technique and Cauchy's test for convergence, time-invariant delays and time-varying delays are considered successively to derive ξ-exponential type sufficient conditions. Based on these, several corollaries about the existence, uniqueness and exponential stability of solutions are obtained. Finally, two numerical examples with time-invariant delays and time-varying delays are given respectively. Their simulated images illustrate the effectiveness of the main theoretical results

Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach

© 2013 IEEE. With the application of quaternion in technology, quaternion-valued neural networks (QVNNs) have attracted many scholars' attention in recent years. For the existing results, dynamical behavior is an important studying side. In this paper, we mainly research the existence, uniqueness and exponential stability criteria of solutions for the QVNNs with discrete time-varying delays and distributed delays by means of generalized 2-norm. In order to avoid the noncommutativity of quaternion multiplication, the QVDNN system is firstly decomposed into four real-number systems by Hamilton rules. Then, we obtain the sufficient criteria for the existence, uniqueness and exponential stability of solutions by special Lyapunov-type functional, Cauchy convergence principle and monotone function. Furthermore, several corollaries are derived from the main results. Finally, we give one numerical example and its simulated figures to illustrate the effectiveness of the obtained conclusion