This paper studies leader-following bounded consensus problem for linear multi-agent systems (MASs) with exogenous disturbances under an observer-based dynamic event-triggered scheme. To guarantee performance requirements, and avoid frequent updates of the sensors, and the controllers at the same time, two independent event-triggered schemes with dynamic threshold are proposed in sensor-to-observer (S-O), and controller-to-actuator (C-A) channels, respectively. And a fully distributed observer event-based controller is designed, which only requires the observer information from neighboring followers, and itself for each follower. With the help of the Riccati equation, and inequality techniques, some simple, and convenient sufficient conditions are derived to ensure that the closed loop system converges to a bounded region exponentially. Moreover, the proposed dynamic event-triggered mechanisms in S-O, and C-A channels do not only lessen the transmission load, and controller update, but also exclude the Zeno behavior. Finally, a numerical example is given to verify the correctness, and efficiency of our results.

This article is concerned with fixed-time synchronization of the nonlinearly coupled neural networks with discontinuous activation and mismatched parameters. First, a novel lemma is proposed to study fixed-time stability, which is less conservative than those in most existing results. Then, based on the new lemma, a discontinuous neural network with mismatched parameters will synchronize to the target state within a settling time via two kinds of unified and simple controllers. The settling time is theoretically estimated, which is independent of the initial values of the considered network. In particular, the estimated settling time is closer to the real synchronization time than those given in the existing literature. Finally, two numerical simulations are presented to illustrate the effectiveness and correctness of our results.

Fixed-time synchronization of complex networks is investigated in this article. First, a completely novel lemma is introduced to prove the fixed-time stability of the equilibrium of a general ordinary differential system, which is less conservative and has a simpler form than those in the existing literature. Then, sufficient conditions are presented to realize synchronization of a complex network (with a target system) within a settling time via three different kinds of simple controllers. In general, controllers designed to achieve fixed-time stability consist of three terms and are discontinuous. However, in our mechanisms, the controllers only contain two terms or even one term and are continuous. Thus, our controllers are simpler and of more practical applicability. Finally, three examples are provided to illustrate the correctness and effectiveness of our results.