Synchronization of hybrid impulsive and switching dynamical networks with delayed impulses

Abstract

In this paper, the exponential synchronization problem is investigated for a class of hybrid impulsive and switching dynamical networks (HISDNs). Different from the existing results concerning synchronization of HISDNs, impulsive input delays are considered in our model. Moreover, in our model, the impulsive instances and system switching instances do not need to be coincident. By using the Razumikhin theorem and the mathematical induction method, several sufficient synchronization criteria are obtained in terms of linear matrix inequalities. The obtained criteria reveal that the frequency of impulsive occurrence, impulsive input delays, can heavily affect the synchronization performance. Finally, an example is provided to illustrate the effectiveness of the obtained results.

Exponential stability of fractional‐order uncertain systems with asynchronous switching and impulses

“…Thus, motivated by the work, 45 the asynchronous switching and impulses is considered in this paper, under this mechanism, impulses can occur not only at the time point of system switching, but also at any other instants, which implies there exist no or multiple impulses between two adjacent switching times, similarly, no or multiple switchings may occur between two adjacent impulsive times (see Figure 2), and thus includes all the cases discussed in the literature. [53][54][55] Lemma 1 (See the work of Zhan et al 45 ). Let nonnegative function V(t) be continuously differentiable on [t 0 , +∞), if there exists 𝜚 ∈  such that…”

“…More precisely, the switching and impulses occur at the same time (see Figure 1), which may lead to some limitations in practical applications. Thus, motivated by the work, 45 the asynchronous switching and impulses is considered in this paper, under this mechanism, impulses can occur not only at the time point of system switching, but also at any other instants, which implies there exist no or multiple impulses between two adjacent switching times, similarly, no or multiple switchings may occur between two adjacent impulsive times (see Figure 2), and thus includes all the cases discussed in the literature 53‐55 …”