Event-Triggered Exponential Stabilization for State-Based Switched Inertial Complex-Valued Neural Networks With Multiple Delays

Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks

This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.

Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks

This article is concerned with stability for stochastic complex-valued delayed complex networks under random denial-of-service (RDoS) attacks. Different from the existing literature on the stability of stochastic complex-valued systems that concentrate on moment stability, we investigate almost sure stability (ASS), where noise plays a stabilizing role. It is noted that, besides the vertex systems influenced by noise, the interactions among vertices are also at the mercy of noise. As a consequence, an innovative noise-based delayed coupling (NDC) in the presence of RDoS attacks is proposed first to accomplish the stability of complex-valued networks, where the RDoS attacks have a certain probability of triumphantly interfering with communications at active intervals of attackers. Namely, RDoS attacks considered are randomly launched at active periods, which is more realistic. In terms of the Lyapunov method and stochastic analysis theory, an almost sure exponential stability (ASES) criterion of the system discussed straightforwardly is developed by constructing a delay-free auxiliary system, while removing the traditional assumption of moment stability. The criterion strongly linked with topological structure, RDoS frequency, attack successful probability, and noise intensity reveals that the higher the noise intensity, the faster the convergence rate is for the stability of the network. In light of the criterion established, we present an algorithm that can be employed to analyze the tolerable attack parameters and the upper bound of the coupling delays, under the prerequisite of guaranteeing the stability of the network. Eventually, the theoretical results are applied to inertial complex-valued neural networks (ICNNs) and an illustrative example is presented to substantiate the efficiency of the theoretical works.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Fixed-Time Stability of Nonlinear Impulsive Systems and its Application to Inertial Neural Networks

This article is concerned with the fixed-time stability (FTS) problem of nonlinear impulsive systems (NISs). By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-dependent settling-time estimation schemes are developed, which fully considers the influence of stabilizing impulses and destabilizing impulses on the convergence rate of the system states. The proposed schemes establish a quantitative relationship between the upper bound of the settling time and impulse effects. It shows that stabilizing impulses can accelerate the convergence rate of the system states and leads to the upper bound of the settling time being smaller. Conversely, destabilizing impulses can reduce it and make the upper bound of the settling time larger. Then, the theoretical results are applied to delayed inertial neural networks (DINNs), where two kinds of controllers are designed to realize fixed-time synchronization of the considered systems in the impulse sense. Finally, some numerical examples are provided to illustrate the validity of the proposed theoretical results.

Global synchronization of complex-valued neural networks with unbounded time-varying delays

This paper investigates global synchronization of complex-valued neural networks (CVNNs) with unbounded time-varying delays. By applying analytical method and inequality techniques, an algebraic criterion is established to ensure global synchronization of the CVNNs via a devised feedback controller, which generalizes some existing outcomes. Finally, two numerical simulations and one application in image encryption are provided to verify the effectiveness of the theoretical results.

State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays

In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.