Guaranteed-performance consensus tracking of singular multiagent systems with Lipschitz nonlinear dynamics and switching topologies

In this paper, the problem of guaranteed-performance consensus tracking of continuous-time singular multiagent systems with Lipschitz nonlinearities and switching topologies is investigated. Consideration is that the interaction of the concerned agent network is described by a set of directed graphs with the union graph having a directed spanning tree rooted at the leader. To establish the guaranteed-performance criterion, a quadratic performance function is constructed by utilizing the consensus errors among all agents. Then, a consensus protocol that collects the local information from neighboring agents is proposed to achieve consensus tracking and to guarantee the consensus regulation performance of the multiagent systems. On the basis of nonsingular transformation approach, singular systems theory, and Lyapunov stability analysis, the concerned guaranteed-performance consensus tracking problem is cast into the admissibility analysis for an equivalent kind of switched singular consensus error system. Furthermore, sufficient conditions on the guaranteed-performance consensus tracking protocol design are formulated in terms of linear matrix inequalities. Finally, numerical examples are employed to demonstrate the effectiveness of the theoretical results.