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

Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Itoˆ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results

Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

summary:In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the $n$-dimensional Clifford-valued neural network into $2^mn$-dimensional real-valued counterparts in order to solve the noncommutativity of Clifford numbers multiplication. Then, we prove the new global asymptotic stability criteria by constructing an appropriate Lyapunov-Krasovskii functionals (LKFs) and employing Jensen's integral inequality together with the reciprocal convex combination method. All the results are proven using linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the achieved results

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example

Global exponential stability conditions for quaternion-valued neural networks with leakage, transmission and distribution delays

This paper studies the global exponential stability problem of quaternion-valued neural networks (QVNNs) with leakage, transmission, and distribution delays. To address this issue, a direct method based on system solutions is proposed to ensure the global exponential stability of the considered network models. In addition, this method does not need to construct any Lyapunov-Krasovskii functional, which greatly reduces the amount of computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results

Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixed-time control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results. © 2020 the Author(s), licensee AIMS Press