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Abstract
The consensus problem is studied in this paper for a class of hybrid switched multi-agent systems (HSMASs) consisted of continuous-time (CT) and discrete-time (DT) subsystems via impulsive control. Due to the complex dynamic characteristics of the system, how to deal with the connection between subsystems at each switching instant is one of the confronted difficulties. Based on the Lyapunov theory, some sufficient consensus criteria are derived under arbitrary switching signals, and we show that the consensus of HSMASs can be achieved with undirected, directed, and switching connected communication networks, respectively. Furthermore, relations between impulsive and sampling instants are discussed, including overlap, stagger, and incomplete overlap. Finally, two numerical examples are presented to illustrate the effectiveness of the main results.
Highlights
Switched systems, consisted of a family of subsystems, are a special case of hybrid systems, and there exists a function called switching law or switching signal that orchestrates the switching among these subsystems [1]–[3]
Many works have been done for dealing with the consensus problem of multi-agent systems (MASs) under different topologies like undirected, directed, and switching graph, The associate editor coordinating the review of this manuscript and approving it for publication was Weiguo Xia
Inspired by the above analysis, in this paper, we aim to study the consensus problem of hybrid switched multi-agent systems (HSMASs) via impulsive control under different topologies and the effects caused by asynchronous samples and impulses
Summary
Switched systems, consisted of a family of subsystems, are a special case of hybrid systems, and there exists a function called switching law or switching signal that orchestrates the switching among these subsystems [1]–[3]. As a basic problem of MASs, the consensus has become an attractive research area in recent years To reach such an agreement, the most common method is to design an appropriate protocol based on the communications among agents, while these communications depend heavily on the network topology. By designing a protocol with information from neighbors, the authors in [9]–[11] presented some necessary and sufficient conditions to reach the agreement of MASs under fixed and switching topologies. For this reason, taking nonlinear dynamics into account, the authors [12], [13] discussed the consensus problem under strongly connected networks Since these designed protocols above always have effects on the MASs, high cost may be caused by continuous and long time information transmission among agents.
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