Event‐triggered H∞$\mathcal {H}_\infty$ synchronization of directed and switched coupled stochastic delayed neural networks with multi‐weights

Abstract

This essay is devoted to studying scriptH∞$\mathcal {H}_\infty$ synchronization problem of directed and switched coupled stochastic delayed neural networks with multi‐weights (SCSDNNMWs) via designing a novel event‐triggered protocol. The proposed model is based on stochastic delayed neural network with directed coupling, and multiple coupling matrices with switching express intricate and changing communication channels. Since the external disturbances are likely to cause network topologies change, fixed and accurate values of coupling matrices are difficult to obtain, while the above model has more advantages of characterizing this real network. Besides, zero eigenvalue of different coupling matrices are represented by the corresponding normalized left eigenvectors (NLEVec), which is hard to establish yet especially when designing necessary Lyapunov functions. The authors' essay deduces that if the Chebyshev distance among NLEVec of multiple coupling matrices is less than a permissible deviation limit based on a weighted set of these NLEVec, then several event‐triggered scriptH∞$\mathcal {H}_\infty$ synchronization and synchronization criteria are established. The effectiveness of these results are verified by several given examples.

Event-triggered synchronization and H∞ synchronization of coupled delayed reaction-diffusion memristive neural networks

“…in which H = (H qp ) N×N denotes the coupling matrix and meets H qq = 0, H qp > 0 when p ∈ N q , t ∈ [t q k , t q k+1 ), the state of node q at t q k is represented by z q (m, t q k ), where t q k corresponds to the event-triggered instant of node q. Similar as the result [15], for any ∈ R > 0, Zeno behavior does not display as t q k+1 − t q k . Let the measure error of triggering event be π q (m, t) = z q (m, t q k ) − z q (m, t).…”

“…Consequently, how to design disturbance attenuating synchronization controllers and reduce the influence of external disturbance has received considerable attention. In recent years, H ∞ synchronization has been verified to be a very effective strategy, which can reduce the effect of disturbances, and important results of CNs have been established [12]- [15], [22]- [25]. In addition, as a discontinuous control strategy, event-triggered control has been widely applied for ensuring CNs synchronization and H ∞ synchronization synchronization [38]- [44] since it can overcome a number of consecutive control's defects in system theory, and avoid some needless communication when data is sent and exchanged for transmission.…”

“…Consequently, how to design disturbance attenuating synchronization controllers and reduce the influence of external disturbance has increasingly become a popular academic topic. In the past few years, H ∞ synchronization has proven to be an efficient strategy in order to reduce the impact of noise or disturbance, and relevant H ∞ synchronization results have been established [12]- [15]. [12] dealt with the H ∞ synchronization problem of chaotic neural networks, and H ∞ synchronization criteria were presented.…”

“…Note that the vast majority of synchronization result in above-mentioned works [6]- [15] have overlooked this diffusive effect in the spatial domain. To the best of our knowledge, the diffusive effect should not be ignored in cellular neural networks [16,17], especially when electrons in a nonuniform electromagnetic domain are highly running.…”

“…As we know, the external disturbance and environmental noise are unavoidable and they are likely to lead the networks to unexpected states, and even break the synchronization. In comparison to existing H ∞ synchronization results [12]- [15], [22]- [25], the event-based mechanism is adopted to study H ∞ synchronization of CDRDMNNs, and the event-triggered H ∞ synchronization problem for the proposed network is firstly solved in our paper. 4.…”