Multi-layer networks, which incorporate multiple subsystems and different kinds of interactions, are recently believed to have a stronger ability in modelling various real-world systems than traditional single-layer complex networks. Motivated by this observation, we try to show how to achieve node-to-node synchronization and complete synchronization in multi-layer networks under directed switching communication topologies, where the nodes have Lur'e type dynamics. First, by using the multiple Lyapunov stability theory, we show that node-to-node synchronization in two-layer networks can be achieved by choosing sufficiently large coupling strength as well as suitable feedback gain matrix if the average dwell time is bounded below by some positive constants. The result is then extended to the case of multiple layers. Furthermore, if the inner communication topologies of each layer have a directed spanning tree with a common root, we show complete synchronization in the considered network can be achieved if the control parameters and the average dwell time are appropriately chosen. Finally, the theoretical results are validated through performing numerical simulations on Chua's circuit with double scroll attractors.

The evolution of the target system (leader) in pinning-controlled complex networks may need to be regulated by some control inputs for performing various practical tasks, e.g., obstacle avoidance, tracking highly maneuverable target, and so on. Motivated by this observation, we shall investigate the global pinning synchronization problems for complex switching networks for which the target system is subject to nonzero control inputs. First, using the idea of unit vector function method, a discontinuous coupling law is designed. With the aid of stability theory for switched systems, it is theoretically shown that synchronization in the network under this discontinuous coupling law can be achieved by choosing sufficiently large coupling strengths if the average dwell time (ADT) is bounded below by a positive constant. Second, we use the boundary layer method to design a continuous-coupling law. It has been theoretically shown that the synchronization error is ultimately uniformly bounded (UUB) under this continuous-coupling law. The chattering effect is also avoided in real implementation by using this continuous-coupling law. Furthermore, for networks with unknown external disturbances and unmodeled dynamics, neuro-adaptive-based coupling laws are designed to ensure that the synchronization error of the networks with undirected switching communication topologies under these laws is UUB. The obtained theoretical results are finally validated by performing numerical simulation on coupling Chua's circuit systems.

This article addresses the consensus disturbance rejection problem for multiple-input multiple-output (MIMO) linear multi-agent systems (MASs) with directed fixed as well as switching communication topologies in the presence of deterministic disturbances. Based on the relative output information among neighboring agents, a controller, which incorporates the consensus error estimator, the state estimator with static coupling strength and the disturbance observer, is given such that consensus tracking could be achieved in the considered MASs under directed switching communication topologies provided that the control parameters are suitably chosen and the average dwell time (ADT) is larger than a positive threshold, whilst the disturbances are fully rejected by the designed disturbance observer. Furthermore, by designing a state estimator with adaptive coupling law, a controller is given such that consensus disturbance rejection of MASs with directed fixed topology could be achieved in a fully distributed manner. The obtained theoretical results are finally validated by performing simulations on the unmanned aerial vehicles (UAVs).

This paper addresses the consensus problem for two-layered MASs (multi-agent systems) subject to attacks on communication edges. Unlike most existing two-layered MAS models, the considered MASs are allowed to have heterogeneous inner communication topologies between the different layers. By using the linear transformation technique, some sufficient criteria are first given to achieve consensus among the leaders within the leader layer where the condition that the interaction topology has directed spanning trees with a fixed root required in most existing works has been removed. Furthermore, based on the relative outputs, observer-based controllers are designed to achieve node-to-node consensus among the two layers. By developing a new kind of multiple Lyapunov function (MLF) based on a bisection search method, some criteria are established under which the node-to-node consensus error will converge into a bounded set asymptotically. It is interestingly found that a less conservative average dwell time (ADT) constraint is obtained for achieving node-to-node consensus by utilizing the proposed MLF compared with that yielded by the traditional MLF constructed from nonsingular M matrix theory. Moreover, we show that consensus can be achieved asymptotically in the layered MASs with the same inner topology subject to synchronous attacks under some suitable conditions. Finally, the effectiveness of the criteria is verified by simulation on networking linear oscillators.

We aim to address the consensus tracking problem for multiple-input-multiple-output (MIMO) linear networked systems under directed switching topologies, where the leader is subject to some nonzero but norm bounded inputs. First, based on the relative outputs, a full-order unknown input observer (UIO) is designed for each agent to track the full states' error among neighboring agents. With the aid of such an observer, a discontinuous feedback protocol is subtly designed. And it is proven that consensus tracking can be achieved in the closed-loop networked system if the average dwell time (ADT) for switching among different interaction graph candidates is larger than a given positive threshold. By using the boundary layer technique, a continuous feedback protocol is skillfully designed and employed. It is shown that the consensus error converges into a bounded set under the designed continuous protocol. Second, as part of the full states' error can be constructed via the agents' outputs, a reduced-order UIO is thus designed based on which discontinuous and continuous feedback protocols are, respectively, proposed. By using the stability theory of the switched systems, it is proven that the consensus error converges asymptotically to 0 under the designed discontinuous protocol, and converges into a bounded set under the designed continuous protocol. Finally, the obtained theoretical results are validated through simulations.