Event-Based Time-Interval Pinning Control for Complex Networks on Time Scales and Applications

Sampled-Data-Based $\mathcal {H}_{\infty }$ Fuzzy Pinning Synchronization of Complex Networked Systems With Adaptive Event-Triggered Communications

“…In this research, for reducing the frequency of internode communications and controller updates, a fuzzy pinning algorithm is developed to determine how many and which nodes should be pinned. Different from [3]- [4], the pinned nodes are related with the adaptive event-triggered mechanism. Moreover, in contrast to the existing related results in [27], a more general time-dependent AETC protocol is proposed in the paper.…”

Synchronization of Complex Dynamical Networks on Time Scales via Pinning Control

“…Lemma 8 (see [40]). For fixed t 0 ∈ T, if p < 0 and p ∈ R + (T, R), then e p (t, t 0 ) ⟶ 0 as t ⟶ ∞, t ∈ T.…”

“…On the other hand, the theory of time scales, a useful tool to deal with continuous and discrete analysis under a unified framework, was introduced by Hilger in his Ph.D. thesis [31]. With the development of the theory of time scales, the synchronization of complex dynamical networks on time scales has received increasing attention [32][33][34][35][36][37][38][39][40]. For example, in 2016, Liu and Zhang [35] studied the synchronization of linear complex dynamical networks on time scales via pinning impulsive control.…”

“…In 2018, Lu et al [39] considered finite-time synchronization of nonlinear complex dynamical networks on time scales via pinning impulsive control. In [40], Xiao, Lewis, and Zeng investigated event-based time-interval pinning control for complex networks on time scales.…”

“…erefore, complex dynamical networks on time scales have great complexity. Moreover, many existing results for continuous-time or discrete-time complex dynamical networks cannot be simply generalized to complex dynamical networks on time scales [35,40].…”