Impulsive control for passivity and exponential synchronization of coupled neural networks with multiple weights

This paper investigates the passivity and synchronization problems for two classes of multiple weighted coupled neural networks (MWCNNs) with or without time delays. Firstly, by utilizing an impulsive control strategy and some inequality techniques, several passivity criteria for MWCNNs with diverse dimensions of output and input are established. Then, based on the Lyapunov functional, some sufficient conditions to ensure the synchronization of MWCNNs via impulsive control are derived. In addition, combined with the comparison principle and the impulsive delay differential inequality, the global exponential synchronization of MWCNNs with time-varying delays is considered under impulsive control. Finally, two numerical examples illustrate the effectiveness of the obtained results.     

Synchronization of coupled heterogeneous complex networks

By only designing the internal coupling, quasi synchronization of heterogeneous complex networks coupled by N nonidentical Duffing-type oscillators without any external controller is investigated in this paper. To achieve quasi synchronization, the average of states of all nodes is designed as the virtual target. Heterogeneous complex networks with two kinds of nonlinear node dynamics are analyzed firstly. Some sufficient conditions on quasi synchronization are obtained without designing any external controller. Quasi synchronization means that the states of all nonidentical nodes will keep a bounded error with the virtual target. Then the heterogeneous complex network with impulsive coupling which means the network only has coupling at some discrete impulsive instants, is further discussed. Some sufficient conditions on heterogeneous complex network with impulsive coupling are derived. Based on these results, heterogeneous complex network can still reach quasi synchronization even if its nodes are only coupled at discrete impulsive instants. Finally, two examples are provided to verify the theoretical results.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Synchronization of stochastic discrete-time complex networks with partial mixed impulsive effects

In this paper, the synchronization problem is studied for a class of stochastic discrete-time complex networks with partial mixed impulsive effects. The involving impulsive effects, called partial mixed impulses, can be regarded as local and time-varying impulses, which means that impulses are not only injected into a fraction of nodes in networks but also contain synchronizing and desynchronizing impulses at the same time. In order to handle this case, several mathematical techniques are proposed to tackle mixed impulsive effects in discrete-time dynamical systems. Based on the variation of parameters formula, several sufficient criteria are derived to ensure that synchronization of the addressed networks can be achieved in mean square. The obtained criteria not only rely on the strengths of mixed impulses and the impulsive intervals, but also can reduce conservativeness. Finally, a numerical example is presented to show the effectiveness of our results for neural networks.     

pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs

This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.     

Synchronization of stochastic perturbed chaotic neural networks with mixed delays

In this paper, we study the synchronization problem of a class of chaotic neural networks with time-varying delays and unbounded distributed delays under stochastic perturbations. By using Lyapunov-Krasovskii functional, drive-response concept, output coupling with delay feedback and linear matrix inequality (LMI) approach, we obtain some sufficient conditions in terms of LMIs ensuring the exponential synchronization of the addressed neural networks. The feedback controllers can be easily obtained by solving the derived LMIs. Moreover, the main results are generalizations of some recent results reported in the literature. A numerical example is also provided to demonstrate the effectiveness and applicability of the obtained results.     

On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays

This paper investigates the problem of designing decentralized impulsive controllers for synchronization of a class of complex dynamical networks (CDNs) about some prescribed goal function. The CDNs are allowed to possess nonidentical nodes and coupling delays. Two cases of time-varying coupling delays are considered: the case where the coupling delays are uniformly bounded, and the case where the derivatives of the coupling delays are not greater than 1. The synchronization analysis for the first case is performed by applying a time-varying Lyapunov function based method combined with Razumikhin-type technique, while the synchronization analysis for the second case is conducted based on a time-varying Lyapunov functional based method. For each case, by utilizing a convex combination technique, the resulting synchronization criterion is formulated as the feasibility problem of a set of linear matrix inequalities (LMIs). Then, sufficient conditions on the existence of a decentralized impulsive controller are presented by employing these newly obtained synchronization criteria. The local impulse gain matrices can be designed by solving a set of LMIs. Finally, two representative examples are given to illustrate the correctness of the theoretical results.     

Stability analysis of stochastic fuzzy Markovian jumping neural networks with leakage delay under impulsive perturbations

This paper investigates the global asymptotic stability of stochastic fuzzy Markovian jumping neural networks with mixed delays under impulsive perturbations in mean square. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delay and continuously distributed delay. By using the Lyapunov functional method, reciprocal convex approach, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.     

Synchronization of linear dynamical networks under stochastic impulsive coupling protocols

This paper investigates a stochastic impulsive coupling protocol for synchronization of linear dynamical networks based on discrete-time sampled-data. The convergence of the networks under the proposed protocol is discussed, and some sufficient conditions are showed to guarantee almost sure exponential synchronization. Moreover, this coupling protocol with a pinning control scheme is developed to lead the state of all nodes to almost sure exponentially converge to a virtual synchronization target. It is shown that the almost sure exponential synchronization can be achieved by only interacting based on the stochastic feedback information at discrete-time instants. Some numerical examples are finally provided to present the effectiveness of the proposed stochastic coupling protocols.     

Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control

This paper addresses the synchronization of stochastic complex networks with time-varying delay via aperiodically intermittent control (AIC). By proposing the concepts of average control ratio and average control frequency for AIC, some new synchronization conditions are obtained, which relax the constraints of the lower bound of control widths and the upper bound of control periods. And the proportion of rest widths can be any value in (0,1). So the constraints on AIC are loosened and thus the conservativeness is reduced compared with the existing related results. Two types of time delay are investigated: (i) the upper bound of time-varying delay should be smaller than the average control width but can be larger than the lower bound of control widths; (ii) the upper bound of time-varying delay has no relationship with control and rest widths. An example of coupled stochastic oscillators systems is presented to show the effectiveness and superiority of our results.     

Exponential synchronization of fractional-order reaction-diffusion coupled neural networks with hybrid delay-dependent impulses

This paper is concentrated on exploring the exponential synchronization of reaction-diffusion coupled neural networks with fractional-order and impulses. Firstly, an extended Halanay-type inequality is established to cope with the hybrid delay-dependent impulsive problem by utilizing the mathematical induction. Furthermore, a direct error method is introduced by constructing Lyapunov function for the addressed networks to investigate the exponential synchronization under impulsive effects. By utilizing the technique of average impulsive interval and strength, some sufficient synchronization criteria are derived, which are closely associated with time delay and the commensurate order for fractional-order systems. Lastly, three numerical examples are presented to demonstrate the correctness for established results.     

Exponential stability of non-linear neutral stochastic delay differential system with generalized delay-dependent impulsive points

This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses.     

Robust exponential stability of uncertain impulsive delay difference equations with continuous time

In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.     

Impulsive effects on weak projective synchronization of parameter mismatched stochastic memristive neural networks

This paper analyses the weak projective synchronization (WPS) of the parameter mismatched memristive neural networks (MNNs) with stochastic disturbance and time delays via impulsive control. Complete synchronization cannot achieve because of the projective factor and mismatched parameters. Therefore, the WPS of practical MNNs under impulsive control strategy is studied. The augmented systems are built to utilize more information of the system and reduce the constraint conditions. Meanwhile, two types of comparison principles are used owing to the impulsive controller with and without time delays. Then, sufficient criteria for the exponential convergence of systems are obtained under the positive and negative effects of impulses. Finally, the validity of the theoretical results is verified by simulations of different conditions.     

Exponential synchronization of multilayer networks with white-noise-based coupling via intermittent periodic event-triggered control

In this paper, the mean-square exponential synchronization of stochastic multilayer networks with white-noise-based time-varying coupling is investigated via intermittent dynamic periodic event-triggered control. The existence of a dynamic term can reduce the number of event triggers. Furthermore, by introducing periodic sampling mechanism, a minimum inter-execution time is guaranteed to avoid Zeno phenomenon. Additionally, by employing Lyapunov method, graph theory, and stochastic analysis techniques, synchronization criteria for multilayer networks under intermittent dynamic periodic event-triggered control are established. To clarify the process of synchronization of multilayer networks, a brief framework is developed on the basis of Tajan’s algorithm. Ultimately, theoretical results are applied into Chua’s circuits and corresponding numerical simulations are given to illustrate the effectiveness and feasibility of the results.     

Passivity-based boundary control for delay reaction-diffusion systems

Passivity-based boundary control is considered for time-varying delay reaction-diffusion systems (DRDSs) with boundary input-output. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are obtained for input strict passivity and output strict passivity of DRDSs, respectively. When the parameter uncertainties appear in DRDSs, sufficient conditions are presented to guarantee the robust passivity. Moreover, we apply our theoretical results to the synchronization problem of coupled delay reaction-diffusion systems and get the criterion to ensure the asymptotic synchronization. Finally, numerical simulations are provided to show the validity of our theoretical results.     

Exponential synchronization of switched genetic oscillators with time-varying delays

This paper addresses the problem of exponential synchronization of switched genetic oscillators with time-varying delays. Switching parameters and three types of nonidentical time-varying delays, that is, the self-delay, the intercellular coupling delay, and the regulatory delay are taken into consideration in genetic oscillators. By utilizing the Kronecker product techniques and ‘delay-partition’ approach, a new Lyapunov–Krasovskii functional is proposed. Then, based on the average dwell time approach, Jensen?s integral inequality, and free-weighting matrix method, delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). These conditions guarantee the exponential synchronization of switched genetic oscillators with time-varying delays whose upper bounds of derivatives are known and unknown, respectively. A numerical example is presented to demonstrate the effectiveness of our results.     

Synchronization of IT2 stochastic fuzzy complex dynamical networks with time-varying delay via fuzzy pinning control

In this paper, the problem of synchronization on interval type-2 (IT2) stochastic fuzzy complex dynamical networks (CDNs) with time-varying delay via fuzzy pinning control is fully studied. Firstly, a more general complex network model is considered, which involves the time-varying delay, IT2 fuzzy and stochastic effects. More specifically, IT2 fuzzy model, as a meaningful fuzzy scheme, is investigated for the first time in CDNs. Then, with the aid of Lyapunov stability theory and stochastic analysis technique, some new sufficient criteria are established to ensure synchronization of the addressed systems. Moreover, on basis of the parallel-distributed compensation (PDC) scheme, two effective fuzzy pinning control protocols are proposed to achieve the synchronization. Finally, a numerical example is performed to illustrate the effectiveness and superiority of the derived theoretical results.     

Intermittent pinning synchronization between two hyperbolic coupled networks with time-varying delays

This paper is devoted to synchronization between two hyperbolic coupled networks (HCNs) with time-varying delays via aperiodically intermittent pinning control (AIPC). Based on the Lyapunov function with a piecewise continuous function, sufficient criteria of HCNs with internal delays only and with hybrid delays are obtained, separately. And it is found that the convergence speed of synchronization of HCNs with hybrid delays is slower than that with internal delays only. Furthermore, two simulation results are presented to verify the theoretical results.     

Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses

This paper addresses the problem of global exponential dissipativity for a class of uncertain discrete-time BAM stochastic neural networks with time-varying delays, Markovian jumping and impulses. By constructing a proper Lyapunov–Krasovskii functional and combining with linear matrix inequality (LMI) technique, several sufficient conditions are derived for verifying the global exponential dissipativity in the mean square of such stochastic discrete-time BAM neural networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. One important feature presented in our paper is that without employing model transformation and free-weighting matrices our obtained result leads to less conservatism. Additionally, three numerical examples with simulation results are provided to show the effectiveness and usefulness of the obtained result.