Swarm stability of linear time‐invariant descriptor compartmental networks

Abstract

Swarm stability is concerned for descriptor compartmental networks with linear time-invariant protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient conditions for both consensus and critical swarm stability are presented, which require a joint matching between the interactive dynamics of nearest neighboring vertices and the Laplacian spectrum of the overall network topology. Three numerical instances are illustrated to verify the theoretical results.

Suboptimal Output Consensus for Time‐Delayed Singular Multi‐Agent Systems

“…However, the singular system is a more natural description of dynamic multi‐agent systems, where the dynamics of each agent may be singular. Especially, normal multi‐agent systems can be regarded as special cases of singular multi‐agent systems, and each agent in some practical multi‐agent systems cannot be described by a normal dynamic system, such as some transistor circuits, multi‐agent supporting systems with each block supported by several pillars and three‐link manipulator networks (see and references therein for more details). By constructing static output feedback consensus protocols, state consensus criteria for singular multi‐agent systems with fixed topologies were proposed in .…”

“…Output consensus analysis and design problems for singular multi‐agent systems were addressed in , where impulse‐free and regular properties cannot be directly guaranteed by associated output consensus criteria. The information delay was not considered in , but it extensively exists in process of information exchanges of neighboring agents and is a critical factor which decides whether or not multi‐agent systems can achieve consensus as shown in .…”

“…Firstly, the current paper models the dynamics of each agent as a singular system, which has more complex structures and special characteristics, while most works focused on output consensus with each agent described by a normal one. Secondly, the current paper realizes the suboptimal tradeoff design between output consensus regulation performances and control energy consumptions, which was not considered in the literatures about singular multi‐agent systems . Thirdly, LMI guaranteed‐cost output consensus and consensualization criteria in the current paper can directly guarantee the regular and impulse‐free properties of singular multi‐agent systems, but it was assumed that each agent is impulse‐free and regular in , where the impacts of the time delay was not considered.…”

Almost decouplability of any directed weighted network topology

“…The motivation of the current work originated from our study on consensus problems for dynamical multi-agent systems [3][4][5][6][7][8]. Consensus implicates that a system achieves certain asymptotic stability even if there are no equilibria, and it actually plays the role like equilibrium of isolated dynamical systems [3][4][5].…”

“…Due to its theoretical importance, the consensus problem has been paid extensive attention by scholars in the area of control theory from various perspectives; see Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein. Particularly, a general framework of the consensus problem for first-order systems is initially proposed in Ref.…”