Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control

Finite‐time synchronization for memristor‐based BAM neural networks with stochastic perturbations and time‐varying delays

“…Remark The proof of Lemma can be found in the work of Wang et al The proof process in the work of the aforementioned authors adopts the method in the work of Chen et al, which is also used in the works of Zhang et al and Yang et al Consider an n ‐dimensional stochastic differential equation where x ( t ) is the n ‐dimensional process on t ≥ 0.…”

“…Remark 2. The proof of Lemma 1 can be found in the work of Wang et al 26 The proof process in the work of the aforementioned authors 26 adopts the method in the work of Chen et al, 51 which is also used in the works of Zhang et al 52 and Yang et al 53 Consider an n-dimensional stochastic differential equation…”

“…This leads to the fact that MNNs are differential equations with discontinuous right sides, and usual method of dealing with MNNs is unsuitable. Recently, the dynamical behaviors of MNNs, including stability and synchronization, have been intensively investigated because of its unique features . In these literature studies, there are some theoretical results about memristor‐based BAMMNs (MBAMNNs), which are the combination of memristor and BAMNNs.…”

“…Recently, the dynamical behaviors of MNNs, including stability and synchronization, have been intensively investigated because of its unique features. [15][16][17][18][19][20][21][22][23][24][25][26] In these literature studies, there are some theoretical results about memristor-based BAMMNs (MBAMNNs), which are the combination of memristor and BAMNNs. For example, Anbuvithya et al studied the nonfragile synchronization for MBAMNNs with two different types of random feedback gain fluctuations and derived some sufficient LMI conditions based on Lyapunov-Krasovskii stability theory 20 ; Li et al 23 investigated the existence and global exponential stability of periodic solution of MBAMNNs with time-varying delays, and obtained some new testable algebraic criteria to guarantee the uniqueness and global exponential stability of periodic solution; Wang et al studied the global asymptotic stability and synchronization of MBAMNNs with leakage delay and time-varying delays and got several LMI-based sufficient conditions by designing sampled-data control strategy.…”

“…For example, Anbuvithya et al studied the nonfragile synchronization for MBAMNNs with two different types of random feedback gain fluctuations and derived some sufficient LMI conditions based on Lyapunov-Krasovskii stability theory 20 ; Li et al 23 investigated the existence and global exponential stability of periodic solution of MBAMNNs with time-varying delays, and obtained some new testable algebraic criteria to guarantee the uniqueness and global exponential stability of periodic solution; Wang et al studied the global asymptotic stability and synchronization of MBAMNNs with leakage delay and time-varying delays and got several LMI-based sufficient conditions by designing sampled-data control strategy. 26 Many dynamical systems depend not only on the current time, but also on the state of the system at some point in the past because signal transmission, physical changes, measurements, etc. This has lead delays.…”