Guaranteed‐performance consensus for nonlinear singular multiagent systems with directed topologies

Abstract

The guaranteed-performance consensus problems for nonlinear singular multiagent systems with directed topologies in both leader-following case and leaderless case are investigated, where the directed interaction topologies contain a directed spanning tree. For situations with and without the leader, two different quadratic performance functions are proposed based on state errors. The state errors in the leader-following case are the state differences between the followers and the leader while in the leaderless case are the state differences between agents with adjacent numbers. First, by exploiting state transformation, the consensus problems are transformed into the stability problems of the corresponding error systems. Second, on the basis of singular systems theory, Laplacian matrix properties, and linear matrix inequality techniques, sufficient conditions for guaranteed-performance consensus are derived for both leaderfollowing and leaderless cases. Third, the explicit expressions of the guaranteed-performance cost are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.