Time-varying Distributed Delays Research Articles

Adaptive finite-time synchronization of quaternion-valued inertial neural networks with mixed delays under quantized event-triggered impulsive strategy

By incorporating inertial terms, quaternions, and time-varying discrete and distributed delays into traditional neural networks (NNs), this paper establishes a category of drive-response quaternion-valued inertial neural networks (QVINNs) with mixed delays. The issue of adaptive finite-time synchronization (FTS) of the QVINNs with mixed delays is explored. To do this, a fresh and low-cost adaptive controller is devised by combining event-triggered impulsive control (ETIC) with quantized control to greatly lower the amount of communication and economic costs. In virtue of the variable substitution, the Lyapunov method, the comparison principle, the inequality technique, and the concept of average impulsive interval (AII), the novel criteria that the QVINNs can accomplish FTS are derived. Meanwhile, it is possible to determine that Zeno-behavior and chattering are absent, and the settling time is predicted. Ultimately, by performing the numerical instance, the efficiency and accuracy of the theoretical results are confirmed.

Fuzzy Adaptive Containment Control for Fractional-Order Heterogeneous Multi-agent Systems with Distributed Time-Varying Delays and Input Saturation

Fuzzy Adaptive Containment Control for Fractional-Order Heterogeneous Multi-agent Systems with Distributed Time-Varying Delays and Input Saturation

Fixed-Time Synchronization for Fractional-Order Cellular Inertial Fuzzy Neural Networks with Mixed Time-Varying Delays

Due to the widespread application of neural networks (NNs), and considering the respective advantages of fractional calculus (FC), inertial neural networks (INNs), cellular neural networks (CNNs), and fuzzy neural networks (FNNs), this paper investigates the fixed-time synchronization (FDTS) issues for a particular category of fractional-order cellular-inertial fuzzy neural networks (FCIFNNs) that involve mixed time-varying delays (MTDs), including both discrete and distributed delays. Firstly, we establish an appropriate transformation variable to reformulate FCIFNNs with MTD into a differential first-order system. Then, utilizing the finite-time stability (FETS) theory and Lyapunov functionals (LFs), we establish some new effective criteria for achieving FDTS of the response system (RS) and drive system (DS). Eventually, we offer two numerical examples to display the effectiveness of our proposed synchronization strategies. Moreover, we also demonstrate the benefits of our approach through an application in image encryption.

Synchronization of Clifford-valued neural networks with leakage, time-varying, and infinite distributed delays on time scales

<abstract><p>Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results.</p></abstract>

Exponential Stability of Impulsive Timescale-Type Nonautonomous Neural Networks With Discrete Time-Varying and Infinite Distributed Delays.

Global exponential stability (GES) for impulsive timescale-type nonautonomous neural networks (ITNNNs) with mixed delays is investigated in this article. Discrete time-varying and infinite distributed delays (DTVIDDs) are taken into consideration. First, an improved timescale-type Halanay inequality is proven by timescale theory. Second, several algebraic inequality criteria are demonstrated by constructing impulse-dependent functions and utilizing timescale analytical techniques. Different from the published works, the theoretical results can be applied to GES for ITNNNs and impulsive stabilization design of timescale-type nonautonomous neural networks (TNNNs) with mixed delays. The improved timescale-type Halanay inequality considers time-varying coefficients and DTVIDDs, which improves and extends some existing ones. GES criteria for ITNNNs cover the stability conditions of discrete-time nonautonomous neural networks (NNs) and continuous-time ones, and these theoretical results hold for NNs with discrete-continuous dynamics. The effectiveness of our new theoretical results is verified by two numerical examples in the end.

Quasi-invariant and attracting sets of competitive neural networks with time-varying and infinite distributed delays

This paper focuses on the quasi-invariant set (QIS), global attracting set (GAS) and global exponential attracting set (GEAS) of competitive neural networks (CNNs) with time-varying and infinite distributed delays. For these purposes, based on the characteristics of nonnegative matrix and M-matrix, a new bidirectional delay integral inequality and a novel integro-differential inequality are first established. From the founded integral inequality, the existence conditions of the QIS and the GAS of the discussed system are obtained. Besides, the existence conditions of the GEAS are also given by the proposed integro-differential inequality, which gets rid of the construction of complex Lyapunov functions and functionals. The frameworks of the QIS, GAS and GEAS are also given. A numerical example is analyzed to confirm the validity of the obtained results in the end.

Sampled Memory-Event-Triggered Fuzzy Load Frequency Control for Wind Power Systems Subject to Outliers and Transmission Delays.

This study is devoted to event-triggered fuzzy load frequency control (LFC) for wind power systems (WPSs) with measurement outliers and transmission delays. Due to the integration of wind turbine (WT) with nonlinearity, the T-S fuzzy model of WPS is established for stability analysis and controller design. To mitigate the network burden, a new sampled memory-event-triggered mechanism (SMETM) related to historical system information is presented. It has the following two merits: 1) the utilization of continuous memory outputs over a given interval is useful to reduce the information loss in the period of samples and the redundant triggering events induced by disturbances and noises and 2) an extra upper constraint is added in the triggering condition to generate a new event only when the error signal belongs to a bounded range, thus, the false events caused by measurement outliers can be differentiated out and then be dropped. By representing the memory signal with transmission delay as a time-varying distributed delay term, a T-S fuzzy time-varying distributed delay system is built up to model the H∞ LFC WPS. With the help of the Lyapunov method and the integral inequality relying on distributed delay, some criteria are derived to solve the triggering matrix and fuzzy controllers. Finally, the merits of the proposed SMETM are tested by simulation results.

ОЦЕНКИ ДЛЯ РЕШЕНИЙ ОДНОГО КЛАССА НЕАВТОНОМНЫХ СИСТЕМ С ПЕРЕМЕННЫМИ СОСРЕДОТОЧЕННЫМ И РАСПРЕДЕЛЕННЫМ ЗАПАЗДЫВАНИЯМИ

We consider a class of  nonautonomous  systems  of  differential  equations with time-varying concentrated and distributed  delays  than  can be unbounded.  Using a Lyapunov–Krasovskii functional, some estimates of solutions are established. The obtained estimates allow us to conclude whether the solutions are stable.

Lagrange Stability of Fuzzy Memristive Neural Networks on Time Scales With Discrete Time Varying and Infinite Distributed Delays

The existing results of Lagrange stability for neural networks with distributed time delays are scale-free, which introduces conservativeness naturally. A class of Takagi–Sugeno fuzzy memristive neural networks (FMNNs) on time scales with discrete time-varying and infinite distributed delays is brought in this article. First, a new scale-limited Halanay inequality is demonstrated by timescale theory. Next, on the basis of inequality techniques on time scales, some new scale-limited algebraic criteria and linear matrix inequality criteria of Lagrange stability are obtained by comparison strategy and generalized Halanay inequality. All scale-limited sufficient criteria of Lagrange stability for FMNNs not only apply to continuous-time FMNNs and their discrete-time analogs, but also could deal with the arbitrary combination of them. Finally, two numerical simulations are given to verify the validity of the obtained theoretical results.

Estimates for solutions to one class of nonlinear nonautonomous systems with time-varying concentrated and distributed delays

Estimates for solutions to one class of nonlinear nonautonomous systems with time-varying concentrated and distributed delays

New results on synchronization for second-order fuzzy memristive neural networks with time-varying and infinite distributed delays

Without converting the second order terms to the first order ones, this article deals with the global asymptotic synchronization of second-order fuzzy memristive neural networks (SFMNNs) with infinite distributed and time-varying delays by contriving feedback control and adaptive control schemes. Based on Lyapunov stability theory, Barbalat Lemma and some analysis strategies, several new criteria in lights of algebraic inequalities are directly acquired to assure the global asymptotic synchronization of the concerned SFMNNs. Besides, compared with the existing reduced-order means, the global asymptotic synchronization is directly analyzed via accepting some new Lyapunov–Krasovskii functionals without the reduced-order means. Ultimately, some examples are provided to identify the availability of the theoretical outcomes.

Synchronization of BAM Cohen--Grossberg FCNNs with mixed time delays

This paper deals with the synchronization problem of bidirectional associative memory (BAM) Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with discrete time-varying and unbounded distributed delays. Some sufficient conditions are obtained to guarantee the robust synchronizationof BAM CGFCNNs with discrete time-varying and unbounded distributed delays subjected to parametric uncertainty by using Lyapunov-Krasovskii (LK) functional and Linear matrix inequality (LMI) approach.Sufficient criteria ensure that the error dynamics of considered system is globally asymptotically stable. Finally, numerical examples with simulations are given to show the efficacy of the derived results.

Disturbance observer–based neural flight control for aircraft with switched time-varying distributed delays

In this article, the high angle of attack (AOA) maneuver control problem is studied under multiple disturbances and uncertainties. For the first time, the switched distributed delay is constructed to characterize the unsteady aerodynamics. Based on neural networks (NNs) and hyperbolic tangent function, the disturbance observer technique is extended to the nonstrict-feedback system control. To handle the switching problem, time-delay problem, and nonstrict-feedback problem caused by switched distributed delay terms, the Lyapunov–Krasovskii (LK) functional method and a variable separation method are cleverly combined. The proposed LK function can relax the constraints on time-varying delay. Finally, a disturbance observer–based neural finite-time prescribed performance flight control law is developed to improve the flight performance at high AOA, and its effectiveness has been verified through rigorous theoretical analysis and simulation experiments.

Exponential stability for delayed complex-valued neural networks with reaction-diffusion terms

In this study, we investigate reaction-diffusion complex-valued neural networks with mixed delays. The mixed delays include both time-varying and infinite distributed delays. Criteria are derived to ensure the existence, uniqueness, and exponential stability of the equilibrium state of the addressed system on the basis of the M-matrix properties and homeomorphism mapping theories as well as the vector Lyapunov function method. The results demonstrate the positive effect of reaction-diffusion on the stability, which further improves the existing conditions. Finally, the analysis of several examples is compared to the present results to verify the correctness and reduced conservatism of the primary results.

Exponential stability of stochastic Hopfield neural network with mixed multiple delays

<abstract> This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results. </abstract>

Standard L1 Stability for Singular Switched Positive Systems with Time-Varying Distributed Delay Under MDRDT Constraint

This paper is concerned with the standard [Formula: see text] stability with respect to singular switched positive systems (SSPSs) with time-varying distributed delays (TVDDs) under mode-dependent ranged dwell time (MDRDT) constraint. Firstly, for SSPSs with TVDDs under MDRDT constraint, a sufficient condition of asymptotical stability is proposed. Next, to analyze disturbance attenuation performance, a sufficient condition of standard [Formula: see text] stability is presented for SSPSs with TVDDs under MDRDT constraint. Via convex optimization approach, the corresponding standard [Formula: see text]-gain performance optimum can be received. In addition, the standard [Formula: see text] stability issue is also extended to the SSPSs in nonsingular case, in delay-free case and in RDT constraint case, respectively. Finally, the validity is proved by giving three examples.

Dissipative stabilization of linear systems with time-varying general distributed delays

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system’s states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovskiĭ functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.

Global exponential synchronization of interval neural networks with mixed delays via delayed impulsive control

This paper investigates the synchronization problem of interval neural networks with both time-varying and unbounded distributed delays under delayed impulsive control. A new impulsive differential inequality which considers the effect of time delays in impulses is proposed. Based on the inequality, several synchronization criteria for interval neural networks are derived by employing impulsive control theory and inequality techniques. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Producing Stable Periodic Solutions of Switched Impulsive Delayed Neural Networks Using a Matrix-Based Cubic Convex Combination Approach.

This article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time-varying delays. First, tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks. Second, a sufficient criterion for the existence, uniqueness, and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse-delay-dependent Lyapunov-Krasovskii functional method. It is worth emphasizing that the addressed Lyapunov-Krasovskii functional covers both triple integral terms and novel quadruple integral terms, which makes the conservatism of the above criteria decrease. Even if the original neural network models are unstable or the impulsive effects are strong, the addressed neural network model can produce a globally exponentially stable periodic solution. These results here, which include boundedness, globally uniformly exponential convergence, and globally exponentially stability of the periodic solution, generalize and improve the earlier publications. Finally, two numerical examples and their computer simulations are given to show the effectiveness of theoretical results.

Synchronization Analysis for Stochastic T-S Fuzzy Complex Networks with Markovian Jumping Parameters and Mixed Time-Varying Delays via Impulsive Control

In this paper, we propose and explore the synchronization examination for fuzzy stochastic complex networks’ Markovian jumping parameters portrayed by Takagi-Sugeno (T-S) fuzzy model with mixed time-varying coupling delays via impulsive control. The hybrid coupling includes time-varying discrete and distributed delays. Based on appropriate Lyapunov–Krasovskii functional (LKF) approach, Newton–Leibniz formula, and Jensen’s inequality, the stochastic examination systems and Kronecker product to create delay-dependent synchronization criteria that guarantee stochastically synchronous of the proposed T-S fuzzy stochastic complex networks with mixed time-varying delays. Adequate conditions for the synchronization criteria for the frameworks are established in terms of linear matrix inequalities (LMIs). At long last, numerical examples and simulations are given to demonstrate the correctness of the hypothetical outcomes.