Saturated and asymmetric saturated control for projective synchronization of inertial neural networks with delays and discontinuous activations through matrix measure method.

The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.

A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks.

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays.

In this article, we discuss bipartite fixed-time synchronization for fractional-order signed neural networks with discontinuous activation patterns. The Filippov multi-map is used to convert the fixed-time stability of the fractional-order general solution into the zero solution of the fractional-order differential inclusions. On the Caputo fractional-order derivative, Lyapunov-Krasovskii functional is proved to possess the indefinite fractional derivatives for fixed-time stability of fragmentary discontinuous systems. Furthermore, the fixed-time stability of the fractional-order discontinuous system is achieved as well as an estimate of the new settling time.. The discontinuous controller is designed for the delayed fractional-order discontinuous signed neural networks with antagonistic interactions and new conditions for permanent fixed-time synchronization of these networks with antagonistic interactions are also provided, as well as the settling time for permanent fixed-time synchronization. Two numerical simulation results are presented to demonstrate the effectiveness of the main results.

Bilateral Teleoperation of Single-Master Multislave Systems With Semi-Markovian Jump Stochastic Interval Time-Varying Delayed Communication Channels.

Communication time delays in a bilateral teleoperation system often carries a stochastic nature, particularly when we have multiple masters or slaves. In this paper, we tackle the problem for a single-master multislave (SMMS) teleoperation system by assuming an asymmetric and semi-Markovian jump protocol for communication of the slaves with the master under time-varying transition rates. A nonlinear robust controller is designed for the system that guarantees its global robust H∞ stochastic stability in the sense of the Lyapunov theory. Employing the nonlinear feedback linearization technique, the dynamics of the closed-loop teleoperator is decoupled into two interconnected subsystems: 1) master-slave tracking dynamics (coordination) and 2) multislave synchronization dynamics. Employing an improved reciprocally convex combination technique, the stability analysis of the closed-loop teleoperator is conducted using the Lyapunov-Krasovskii methodology, and the stability conditions are expressed in the form of linear matrix inequalities that can be solved efficiently using numerical algorithms. Numerical studies and simulation results validate the effectiveness of the proposed controller design algorithm in both tracking and synchronization performance of the SMMS system, and robustly handling the stochastic and nondifferentiable nature of communication delays.

Delayed state-feedback control for stabilization of neural networks with leakage delay.

This paper mainly deals with the problem of designing delayed state-feedback controller for neural networks with leakage delay. By constructing an appropriate Lyapunov-Krasovskii functional including double integral terms having two different exponential decay rates and utilizing linear matrix inequality (LMI) technique with the help of slack variables, some sufficient conditions for globally exponential stabilization results are obtained by designing of delayed state-feedback controller. The novelty of this paper includes: (i) although many papers dealt with dynamics of neural networks with leakage delay, there is little work on design of feedback controller. Even there is almost no result that deals with the delay-feedback controller for such delay systems, which is the main motivation of this paper; (ii) the derived delay-dependent stability criteria establish the relationship between leakage delay and time delay in the feedback term, which can be easily checked via the MATLAB LMI toolbox; (iii) we consider the general case that the control term is given in the form of Bu, where B is an n×m real matrix. Such case is more difficult to handle than the special case that B is unit matrix. It indicates that the controller can be used in all states or in some states by proper selection of the matrix B. The effectiveness of the proposed method in this paper is illustrated via numerical examples.

Event-triggered H∞ state estimation for semi-Markov jumping discrete-time neural networks with quantization.

This paper investigates H∞ state estimation problem for a class of semi-Markovian jumping discrete-time neural networks model with event-triggered scheme and quantization. First, a new event-triggered communication scheme is introduced to determine whether or not the current sampled sensor data should be broad-casted and transmitted to the quantizer, which can save the limited communication resource. Second, a novel communication framework is employed by the logarithmic quantizer that quantifies and reduces the data transmission rate in the network, which apparently improves the communication efficiency of networks. Third, a stabilization criterion is derived based on the sufficient condition which guarantees a prescribed H∞ performance level in the estimation error system in terms of the linear matrix inequalities. Finally, numerical simulations are given to illustrate the correctness of the proposed scheme.

Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach.

This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay.

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable.

Stability and synchronization analysis of inertial memristive neural networks with time delays.

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

Analysis of global O(t(-α)) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays.

In this paper, the problem of the global O(t(-α)) stability and global asymptotic periodicity for a class of fractional-order complex-valued neural networks (FCVNNs) with time varying delays is investigated. By constructing suitable Lyapunov functionals and a Leibniz rule for fractional differentiation, some new sufficient conditions are established to ensure that the addressed FCVNNs are globally O(t(-α)) stable. Moreover, some sufficient conditions for the global asymptotic periodicity of the addressed FCVNNs with time varying delays are derived, showing that all solutions converge to the same periodic function. Finally, numerical examples are given to demonstrate the effectiveness and usefulness of our theoretical results.

Finite-time synchronization of fractional-order memristor-based neural networks with time delays.

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results.

Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach.

This paper studies the impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable. The aim of this paper is to obtain the synchronization criteria, which is suitable for both exactly known and partly unknown transition probabilities such that the coupled neural network is synchronized with mixed time-delay. The considered impulsive effects can be synchronized at partly unknown transition probabilities. Besides, a multiple integral approach is also proposed to strengthen the Markovian jumping randomly coupled neural networks with partly unknown transition probabilities. By making use of Kronecker product and some useful integral inequalities, a novel Lyapunov-Krasovskii functional was designed for handling the coupled neural network with mixed delay and then impulsive synchronization criteria are solvable in a set of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results.

Stability analysis of memristor-based fractional-order neural networks with different memductance functions.

In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of memductance functions is extensively investigated. Moreover, we formulate the complex-valued memristor-based fractional-order neural networks (CVMFNNs) with two different types of memductance functions and analyze the existence, uniqueness and uniform stability of such networks. By using Banach contraction principle and analysis technique, some sufficient conditions are obtained to ensure the existence, uniqueness and uniform stability of the considered MFNNs and CVMFNNs with two different types of memductance functions. The analysis results establish from the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, four numerical examples are presented to show the effectiveness of our theoretical results.

Further analysis of global µ-stability of complex-valued neural networks with unbounded time-varying delays.

In this paper, we consider the problem of global µ-stability for complex-valued neural networks (CVNNs) with unbounded time-varying delays and it has been widely investigated. Under mild conditions, some new sufficient conditions for global µ-stability of considered CVNNs are derived. Moreover, some new sufficient conditions are obtained to ensure the global µ-stability of CVNNs in the form of complex-valued LMIs as well as real-valued LMIs by using an appropriate Lyapunov-Krasovskii functional and linear matrix inequalities (LMIs). Both of complex-valued LMIs as well as real-valued LMIs are easily solved by using standard numerical algorithms. Finally, two numerical examples are presented to demonstrate the effectiveness and usefulness of our theoretical results.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.

Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays.

This paper deals with the problem of existence and uniform stability analysis of fractional-order complex-valued neural networks with constant time delays. Complex-valued recurrent neural networks is an extension of real-valued recurrent neural networks that includes complex-valued states, connection weights, or activation functions. This paper explains sufficient condition for the existence and uniform stability analysis of such networks. Three numerical simulations are delineated to substantiate the effectiveness of the theoretical results.

Non-fragile robust synchronization for Markovian jumping chaotic neural networks of neutral-type with randomly occurring uncertainties and mode-dependent time-varying delays.

This paper deals with the problem of robust synchronization for uncertain chaotic neutral-type Markovian jumping neural networks with randomly occurring uncertainties and randomly occurring control gain fluctuations. Then, a sufficient condition is proposed for the existence of non-fragile output controller in terms of linear matrix inequalities (LMIs). Uncertainty terms are separately taken into consideration. This network involves both mode dependent discrete and mode dependent distributed time-varying delays. Based on the Lyapunov-Krasovskii functional (LKF) with new triple integral terms, convex combination technique and free-weighting matrices method, delay-dependent sufficient conditions for the solvability of these problems are established in terms of LMIs. Furthermore, the problem of non-fragile robust synchronization is reduced to the optimization problem involving LMIs, and the detailed algorithm for solving the restricted LMIs is given. Numerical examples are provided to show the effectiveness of the proposed theoretical results.

Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach.

We extend the notion of Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Some sufficient conditions are obtained to guarantee the synchronization of the memristor-based recurrent neural networks via delay-dependent output feedback controller in terms of linear matrix inequalities (LMIs). The activation functions are assumed to be of further common descriptions, which take a broad view and recover many of those existing methods. A Lyapunov-Krasovskii functional (LKF) with triple-integral terms is addressed in this paper to condense conservatism in the synchronization of systems with additive time-varying delays. Jensen's inequality is applied in partitioning the double integral terms in the derivation of LMIs and then a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters has emerged. Meanwhile, this paper puts forward a well-organized method to manipulate such a combination by extending the lower bound lemma. The obtained conditions not only have less conservatism but also less decision variables than existing results. Finally, numerical results and its simulations are given to show the effectiveness of the proposed memristor-based synchronization control scheme.

Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays.

In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov-Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.