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In this article, we investigate the global uniform exponential stability problem of linear time‐varying systems with delayed impulsive effects. Two cases are considered: in the first case, the impulse‐free system is uniformly asymptotically stable and in the second case, the impulse‐free system may not be uniformly asymptotically stable. When the impulse‐free system is uniformly asymptotically stable, by the virtue of a uniformly asymptotically stable function, Lyapunov‐based sufficient conditions are derived to ensure the uniform exponential stability of linear time‐varying systems, where destabilizing and stabilizing impulses are considered, respectively. Different from existing results, the Lyapunov function is not assumed to decrease all the time and it is shown that under some conditions, the delayed impulsive effects are stabilizing. For the case that the impulse‐free system is not uniformly asymptotically stable, a time‐varying function is used to characterize the upper bound on the derivative of the Lyapunov function, and it is illustrated that the linear time‐varying systems can be stabilized by the delayed impulsive effects. Moreover, it is also shown that the impulsive input delay‐dependent criteria are less conservative than the delay‐independent ones when the impulsive input delay is small. Some examples are presented to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the sampled-data consensus problem for a class of nonlinear multiagent systems subject to cyber attacks. The considered attacks are assumed to be recoverable, which destroy the connectivity of the network topology with directed spanning tree. In light of the designed sampled-data control protocol, a more general switched system is proposed to model both the cyber attacks and the sampled-data mechanism within a unified framework. Then, by using the contradiction methods, the solution of a class of differential equations is provided to deal with the technical challenge resulting from the switching and sampling issues. Furthermore, in terms of such a solution combined with the constructed piecewise Lyapunov function, sufficient conditions are derived under which the nonlinear multiagent systems subject to attacks achieve the consensus exponentially. The relationship between the attack frequency and the sampling period is also revealed through the obtained conditions. Finally, simulations are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]