Unbounded Distributed Delays Research Articles

Existence and exponential stability of a periodic solution of an infinite delay differential system with applications to Cohen–Grossberg neural networks

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincidence degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen–Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and two numerical examples to illustrate the effectiveness of some of our results.

Submission to Special Issue to Explainable Representation Learning-Based Intelligent Inspection and Maintenance of Complex Systems: Synchronization of Inertial Neural Networks With Unbounded Delays via Sampled-Data Control.

This article addresses the synchronization issue for inertial neural networks (INNs) with heterogeneous time-varying delays and unbounded distributed delays, in which the state quantization is considered. First, by fully considering the delay and sampling time point information, a modified looped-functional is proposed for the synchronization error system. Compared with the existing Lyapunov-Krasovskii functional (LKF), the proposed functional contains the sawtooth structure term V8(t) and the time-varying terms ex(t-βħ (t)) and ey(t-βħ (t)) . Then, the obtained constraints may be further relaxed. Based on the functional and integral inequality, less conservative synchronization criteria are derived as the basis of controller design. In addition, the required quantized sampled-data controller is proposed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness and superiority of the proposed scheme in this article.

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

In this paper, the global exponential stability of quaternion BAM neural networks with mixed delays is investigated. The involved delays include multiple time‐varying transmission delays and unbounded distributed delays. Existence and uniqueness of equilibrium point of the considered neural networks are investigated by using the homeomorphism theory between topology spaces. To show sufficient conditions for global exponential stability of the unique equilibrium point, a method based on estimation of solutions is presented. The acquired stability conditions contain only several simple linear scalar inequalities, which can be easily solved. The availability of theoretical results is shown by a numerical example. A point worth emphasizing is that the method based on estimation of solutions is applicable for models of many time‐delay systems after a minor modification.

Formation-Containment Tracking for Heterogeneous Linear Multiagent Systems Under Unbounded Distributed Transmission Delays

This article considers the formation-containment tracking problem of heterogeneous linear multiagent systems with unbounded distributed transmission delays. The multiagent system under consideration consists of a reference leader with a desired trajectory, a group of formation-leaders with a prescribed formation, and a group of followers. Novel distributed control laws are proposed for the formation-leaders and followers, respectively. It is shown that under the proposed control laws, the outputs of the formation-leaders not only achieve a prescribed time-varying formation but also track the desired trajectory generated by the reference leader, while the output of each follower converges to the convex hull spanned by the outputs of those formation-leaders. It should be pointed out that many existing results on consensus tracking, formation tracking, and containment control of linear multiagent systems with constant or bounded distributed transmission delays are included as special cases of our results. Finally, a numerical example is given to illustrate the effectiveness of the proposed controllers.

Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

In this paper, the synchronization control problem of high-order quaternion Hopfield neural networks (HOQHNNs) with unbounded distributed delays and time-varying discrete delays is studied. Since the non-exchangeability of quaternion multiplication operation, the error system is first decomposed into equivalent real-valued systems, and then the driving-response structure of HOQHNN is achieved exponential synchronization by designing a state feedback controller. At the same time, two examples are offered to illustrate the applicability of the consequences obtained. Finally, the obtained global exponential synchronization criterion is applied to encrypt and decrypt color images. The method proposed here has four advantages: (1) There is no need to construct any Lyapunov–Krasovskii functional, which is straight in the light of the definition of global exponential synchronization; (2) The obtained synchronization criterion contains only a few simple inequalities, which can find the solutions readily; (3) The proposed method is available to real-valued and complex-valued neural networks; (4) The obtained results are helpful for the image secure transmission.

Dynamics of continuous-time recurrent neural networks with random connection weights and unbounded distributed delays

Dynamics of continuous-time recurrent neural networks with random connection weights and unbounded distributed delays

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.

Robust Cooperative Output Regulation of Heterogeneous Uncertain Linear Multiagent Systems With Unbounded Distributed Transmission Delays

This article studies the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems under unbounded distributed transmission delays. A novel distributed observer is first proposed to estimate the state of an exosystem in the presence of unbounded distributed transmission delays. Then, two novel distributed controllers, one based on state feedback and the other based on output feedback, are further developed without any prior knowledge of the unbounded transmission delays. It is shown that the resulting closed-loop multiagent systems can achieve robust cooperative output regulation. It is also shown that the better transient performance is achieved with our proposed controllers in contrast to many existing low-gain controllers, which are proposed to deal with both bounded and unbounded transmission delays. Our results can be directly applied to solve cooperative output regulation problems of multiagent systems with bounded distributed or constant transmission delays. Furthermore, our results can also be directly applied to solve leader–following consensus problems of multiagent systems with unbounded distributed, bounded distributed, or constant transmission delays. Finally, a simulation example is provided to illustrate the effectiveness of the proposed controllers.

Output Containment Control of Heterogeneous Linear Multiagent Systems With Unbounded Distributed Transmission Delays.

In this article, the output containment control problem of heterogeneous linear multiagent systems (MASs) with unbounded distributed transmission delays is considered. A key technical lemma is first established to show that the distributed observers under unbounded distributed transmission delays can be utilized to estimate the convex combination of the states of multiple leaders. Then, a novel distributed output feedback control law is proposed based on those distributed observers. It is shown that under our proposed control law, the output of each follower converges to the convex hull spanned by the outputs of the leaders. In addition, our results include relevant results on output containment control of MASs with bounded distributed or constant transmission delays as special cases. Finally, the effectiveness of the proposed control law is demonstrated by a simulation example.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

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.

Existence, uniqueness, and global asymptotic stability of an equilibrium in a multiple unbounded distributed delay network

By employing the notion of M-matrices and Banach’s contraction mapping principle, we provide complete characterisation of the existence and uniqueness of an equilibrium of a Cohen–Grossberg–Hopfield-type neural network endowed with multiple unbounded distributed time delays. Invoking similar arguments, and by constructing a suitable Lyapunov functional, we establish sufficient conditions for the global asymptotic stability of the equilibrium, independent of time delays.

Global exponential stability analysis of discrete-time genetic regulatory networks with time-varying discrete delays and unbounded distributed delays

This paper addresses the problem of exponential stability analysis of discrete-time genetic regulatory networks (GRNs) with time-varying discrete delays and unbounded distributed delays. A novel approach is proposed to establish delay-dependent and -independent global exponential stability criteria for the class of GRNs under consideration. The main novelties lie in: (i) without any auxiliary function or Lyapunov–Krasovskii functional is required in the process of deriving the global exponential stability criteria; (ii) the obtained stability criteria improves or generalizes the existing results; (iii) the obtained stability criteria are directly represented by the systems parameters, which can be conveniently verified; and (iv) the exponential estimation of GRNs can be obtained from the derivation process of the exponential stability criteria. The effectiveness of theoretical results is illustrated by presenting several numerical examples.

Convergence on non-autonomous inertial neural networks with unbounded distributed delays

ABSTRACTIn this paper, without using reduced-order method, a class of non-autonomous inertial neural networks with time-varying connection weights and unbounded continuously distributed delays are considered. Based upon Lyapunov function method and differential inequality technique, some sufficient conditions are established to reveal that all solutions of the addressed model and their derivatives converge to zero vector, which extend and complement earlier ones in the literature. Moreover, a numerical example is provided to illustrate the correctness of the theoretical results.

Exponential synchronization of coupled neutral-type neural networks with mixed delays via quantized output control

In this paper, new control scheme is considered for exponential synchronization of coupled neutral-type neural networks (NTNNs) with both bounded discrete-time delay and unbounded distributed delay (mixed delays). It is assumed that only the measured output can be utilized to design the controller. Quantized output controllers (QOCs) are considered to save the bits rate of communication channels and the bandwidth. The main difficulty in solving this problem is to cope with the neutral terms, the delays, and the uncertainties induced by the quantization simultaneously. By designing new Lyapunov–Krasovskii functionals and proposing novel analytical techniques, sufficient conditions are derived to ensure the exponential synchronization of the interested NTNNs. The control gains are given by solving a set of linear matrix inequalities (LMIs), which are not necessarily to be negative-definite matrices. Numerical examples are provided to verify the effectiveness and merits of the proposed approach.

Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays

This paper investigates the stability and stabilization of inertial memristive neural networks (IMNNs) with discrete and unbounded distributed delays. The considered IMNNs are described as hybrid neural systems with second-order derivatives due to the combination of memristor and inertial items. By invoking an appropriate variable substitution method, the hybrid neural system is turned into a first-order differential system. Then, based on the nonsmooth analysis and Lyapunov stability theories, several new algebraic conditions for the global stability of IMNNs with unbounded distributed delays are derived. In addition, two simple classes of feedback control laws are designed for the considered IMNNs and the corresponding stabilizability criteria are established. Finally, two numerical examples and their discussions are provided to illustrate the validity and superiority of the theoretical results.

Synchronization of memristive neural networks with mixed delays via quantized intermittent control

It is well known that how to deal with the effect of time delay and how to determine the control and rest widths are the main difficulties for intermittent control. This paper considers asymptotic synchronization of drive-response memristive neural networks (MNNs) with bounded time-varying discrete delay and unbounded distributed delay (mixed delays), which extends existing intermittent control techniques and reveals new relationship between control width and rest width. A quantized intermittent control (QIC) is designed to save both channel resources and control cost and reduce both the amount of transmitted information and channel blocking. Based on weighted double-integral inequalities, novel Lyapunov–Krasovskii functionals with negative terms are designed, which reduce the conservativeness of obtained results greatly. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to ensure the asymptotic synchronization. The control gains can also be designed by solving the LMIs. It is shown that the QIC can be neither periodic nor proportional between control width and rest width. Moreover, the relationships between control width, rest width, and convergence rate are explicitly given. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays

This paper deals with the stabilization problem of memristive recurrent neural networks with inertial items, discrete delays, bounded and unbounded distributed delays. First, for inertial memristive recurrent neural networks (IMRNNs) with second-order derivatives of states, an appropriate variable substitution method is invoked to transfer IMRNNs into a first-order differential form. Then, based on nonsmooth analysis theory, several algebraic criteria are established for the global stabilizability of IMRNNs under proposed feedback control, where the cases with both bounded and unbounded distributed delays are successfully addressed. Finally, the theoretical results are illustrated via the numerical simulations.

Impulsive pinning control algorithm of stochastic multi-agent systems with unbounded distributed delays

The mean square exponential consensus problem for stochastic multi-agent systems with unbounded distributed delays is investigated. Two delayed impulsive pinning control protocols are proposed that are different from those of existing delay-free impulsive pinning controllers. By employing the Lyapunov function method, sufficient conditions are constructed under the presented strategies. It is shown that the system can realize mean square exponential consensus by controlling a small portion of agents. Then, the simulations indicate that the scheme is both feasible and effective.

Global µ-stability of quaternion-valued neural networks with mixed time-varying delays

In this paper, the problem of global µ-stability for quaternion-valued neural networks with time-varying delays and unbounded distributed delays is investigated. To avoid the non-commutativity of quaternion multiplication, the quaternion-valued neural networks is decomposed into two complex-valued systems. By employing the homomorphic mapping principle, a sufficient condition for the existence and uniqueness of equilibrium point of the considered quaternion-valued neural networks is proposed in the form of linear matrix inequality (LMI) in complex-valued domain. Further, the appropriate Lyapunov–Krasovkii functional is constructed in the Hermitian quadratic form, and sufficient condition to ensure the global µ-stability of the equilibrium point is obtained by using inequality technique. Finally, two numerical examples with simulations are provided to verify the effectiveness of the obtained results.