The current paper investigates energy-constraint formation design and analysis problems for multiagent systems with two types of switching interaction topologies; that is, leaderless ones and leader-following ones. Firstly, a new formation control protocol with switching interaction topologies is shown, where the whole energy supply is limited previously. Then, by constructing the relationship of the whole energy supply and the matrix variable, sufficient conditions for leaderless energy-constraint formation design and analysis are respectively presented by the linear matrix inequality tool. Furthermore, an approach is proposed to determine an explicit expression of the formation center function, which determines the macroscopic motion of a multiagent system as a whole and consists of two parts: the initial state term and the formation function term. Moreover, main conclusions of leaderless energy-constraint formation are extended into leader-following multiagent systems by a new two-step transformation approach, where the asymmetric structure feature of leader-following switching interaction topologies is well dealt with. Finally, two numerical examples are provided to demonstrate the effectiveness of main conclusions.

The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.

This article deals with limited-budget output consensus for descriptor multiagent systems with two types of switching communication topologies, that is, switching connected ones and jointly connected ones. First, a singular dynamic output feedback control protocol with switching communication topologies is proposed on the basis of the observable decomposition, where an energy constraint is involved and protocol states of neighboring agents are utilized to derive a new two-step design approach of gain matrices. Then, limited-budget output consensus problems are transformed into asymptotic stability ones and a valid candidate of the output consensus function is determined. Furthermore, sufficient conditions for limited-budget output consensus design and analysis for two types of switching communication topologies are proposed, respectively, and an explicit expression of the output consensus function is given, which is identical for two types of switching communication topologies. Finally, two numerical simulations are shown to demonstrate theoretical conclusions.