Pth Moment Exponential Synchronization Research Articles

Pth Moment Exponential Synchronization for Delayed Multi-Agent Systems With Lévy Noise and Markov Switching

<i>P</i>th Moment Exponential Synchronization for Delayed Multi-Agent Systems With Lévy Noise and Markov Switching

Aperiodically synchronization of multi-links delayed complex networks with semi-Markov jump and their numerical simulations to single-link robot arms

This paper investigates the pth moment exponential synchronization problem of multi-links stochastic delayed complex networks with semi-Markov jump via aperiodically intermittent control. Combining random disturbances, time-varying delay and semi-Markov jump with multi-links systems, our work is more relevant than previous work. Based on Lyapunov method and graph theory, a novel inequality for disposing of the problem of pth exponential synchronization is established under the aperiodically intermittent control and some sufficient criteria are derived. The theoretical results supply a new perspective showing the synchronization criterion and the topological structure of multi-links systems related closely. Furthermore, the value of our results is exhibited by applying them to the single-link robot arms in engineering. Eventually, a numerical simulation is provided to demonstrate the validity of our results.

Existence and synchronization of coupled stochastic infinite-dimensional systems via aperiodically intermittent control

This paper analyzes a class of stochastic coupled systems with time-varying delays in infinite dimensions. The existence and uniqueness as a prerequisite to ensure synchronization of the solution is analyzed, based on the idea of the contraction mapping principle, graph theory, and mild Itô's formula. Next, the p-th moment exponential synchronization (PMES) of infinite-dimensional systems is realised using the discrete control strategy, namely, aperiodically intermittent control (AIC). By combining graph theory with the Lyapunov method, several criteria for synchronizing infinite-dimensional systems are obtained using the mild Itô's formula. These criteria show the effects of control parameters, topology, and time delays on PMES. Finally, the theoretical results are applied to a class of neural networks with reaction-diffusion, and some numerical simulations are also given.

The pth Moment Exponential Synchronization of Drive-Response Memristor Neural Networks Subject to Stochastic Perturbations

In this paper, the p t h moment exponential synchronization problems of drive-response stochastic memristor neural networks are studied via a state feedback controller. The dynamics of the memristor neural network are nonidentical, consisting of both asymmetrically nondelayed and delayed coupled, state-dependent, and subject to exogenous stochastic perturbations. The pth moment exponential synchronization of these drive-response stochastic memristor neural networks is guaranteed under some testable and computable sufficient conditions utilizing differential inclusion theory and Filippov regularization. Finally, the correctness and effectiveness of our theoretical results are demonstrated through a numerical example.

Event-triggered delayed impulsive control for synchronization of stochastic complex networks under deception attacks

This paper analyzes a class of stochastic complex networks (SCNs) subjected to deception attacks via the event- triggered delayed impulsive control (ETDIC) strategy. Noting the universality of delay, we consider the delay in impulsive control. The impulse is combined with the event-triggered mechanism (ETM), that is, the impulsive instant is determined by the ETM, which is defined by the network topology and the Lyapunov function. Based on this ETM, through a combination of the Lipschitz-Razumikhin method and graph theory, we obtain the conditions to avoid Zeno behavior and give some criteria of pth moment exponential synchronization (PMES) for SCNs under deception attacks. The criteria are related to the topology of the network, the event-triggered parameters, and the attack signals sent by the enemy. Finally, we analyze a class of coupling Chua’s circuits subjected to deception attacks and present numerical examples to verify the validity and practicability of our theoretical results.

Formula omitted]th moment synchronization of stochastic impulsive neural networks with time-varying coefficients and unbounded delays

This article is devoted to the investigation of the pth moment synchronization problem for stochastic impulsive neural networks (SINNs) with time-varying coefficients and unbounded delays. First of all, one novel impulse generation rule is proposed, which generates the more general impulsive sequences. In order to cope with time-varying coefficients, unbounded delays and impulsive disturbances, some impulsive differential inequalities are developed by utilizing the comparison principle. With the help of the established impulsive inequalities, the synchronization of SINNs is analyzed in detail, and both pth moment exponential synchronization and asymptotical synchronization are realized by designing appropriate feedback controllers. Finally, several simulation examples are provided to illustrate the validity of the theoretical results.

Intermittent Control Strategy for Synchronization Analysis of Time-Varying Complex Dynamical Networks

The pth moment exponential synchronization (PMES) problem for time-varying complex dynamical networks (CDNs) with multiple time-varying delays (TCDNMTDs) by aperiodically intermittent control is studied in this paper. Compared with related work, the coupling structure of CDNs is time varying. Also, internal time-varying delays and coupling time-varying delays are taken into consideration and they are different from each other. It is worth emphasizing that the intermittent control scheme proposed here is nonperiodical. Some criteria are derived to make TCDNMTDs achieve PMES by using the Lyapunov method and graph theory. Additionally, we also consider the synchronization of second-order Kuramoto oscillators and coupled Chua's circuits and some numerical simulations are presented to verify the validity of our results.

Synchronization of stochastic multiple weighted coupled networks with Markovian switching

We investigate the synchronization of stochastic multiple weighted coupled networks with Markovian switching (SMWCNMS). By designing an appropriate controller, we obtain several sufficient criteria ensuring the pth moment exponential synchronization and almost surely exponential synchronization for SMWCNMS based on graph theory. Moreover, we also investigate the pth moment asymptotical synchronization and almost surely asymptotical synchronization for SMWCNMS. Finally, we provide a numerical example to illustrate the availability of the proposed synchronization criteria.

More general results of aperiodically intermittent synchronization for stochastic Markovian switching complex networks with multi-links and time-varying coupling structure

The paper is concerned with the pth moment exponential synchronization for stochastic Markovian switching complex networks with multi-links via aperiodically intermittent control. Different from the current literature on multi-links systems, the networks we consider have time-varying topology structure. New differential inequalities are established in which the Markovian switching and multiple time-varying delays are taken into account and the constraint on parameter that determines exponential convergence rate is reduced. Based on Lyapunov method, graph theory and differential inequality techniques, some sufficient conditions are obtained to achieve exponential synchronization. As a result, the developed synchronization criteria have more accurate exponential convergence rate than that in most existing literature which focuses on delayed systems with intermittent control. Finally, an application to modified Chua’s circuits and corresponding numerical simulations are presented to demonstrate the effectiveness of the proposed theoretical results.

Aperiodically intermittent synchronization of Markovian jump stochastic complex networks with time-varying delays

ABSTRACT In this paper, pth-moment exponential synchronization for Markovian jump stochastic complex networks with time-varying delays (MJSCNTVDs) is studied via aperiodically intermittent control. By combining graph theory and -matrix theory, some novel synchronization criteria are derived, which comprise two forms: (1) Lyapunov-type criteria and (2) coefficient-type criteria. As its applications, the obtained synchronization results are applied to explore pth-moment exponential synchronization of stochastic coupled oscillators with time-varying delays and Markovian jump. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required and that the restriction between control width and delay is removed. Two numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.

Synchronization of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions and unbounded delays

In this paper, synchronization of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions and unbounded discrete time-varying delays is investigated. By virtue of theories of partial differential equations, inequality methods, and stochastic analysis techniques, pth moment exponential synchronization and almost sure exponential synchronization of the underlying neural networks are developed. The obtained results in this study enhance and generalize some earlier ones. The effectiveness and merits of the theoretical criteria are substantiated by two numerical simulations.

Exponential synchronization of stochastic coupled oscillators networks with delays

This paper investigates the exponential synchronization problem of coupled oscillators networks with disturbances and time-varying delays. On basis of graph theory and stochastic analysis theory, a feedback control law is designed to achieve exponential synchronization. By constructing a global Lyapunov function for error network, both pth moment exponential synchronization and almost sure exponential synchronization of drive-response networks are obtained. Finally, a numerical example is given to show the effectiveness of the proposed criteria.

Pth moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching

This paper is a contribution to the analysis of the pth moment exponential synchronization problem for a class of stochastic delayed Cohen–Grossberg neural networks with Markovian switching. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the delays are time-varying delays. By using the Lyapunov–Krasovskii functional, stochastic analysis theory, a generalized Halanay-type inequality as well as output coupling with delay feedback control technique, some novel sufficient conditions are derived to achieve complete pth moment exponential synchronization of the addressed neural networks. In particular, the traditional assumptions on the differentiability of the time varying delay and the boundedness of its derivative are removed in this paper. The results obtained in this paper generalize and improve many known results. Moreover, a numerical example and its simulation are also provided to demonstrate the effectiveness and applicability of the theoretical results.

Pth moment exponential synchronization analysis for a class of stochastic neural networks with mixed delays

In this paper, the issue of pth moment exponential synchronization of a class of stochastic neural networks with mixed delays is investigated. By establishing two new integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential synchronization are obtained. Compared with previous method, our method does not resort to any Lyapunov function. The results obtained in this paper generalize some earlier works reported in the literature. Some strict constraints of time delays and kernel functions are removed. Two numerical examples are presented to illustrate the validity of the main results.