Cooperative tracking of networked agents with a high-dimensional leader: Qualitative analysis and performance evaluation

Cooperative consensus tracking and its L₂-gain performance is investigated in this paper for a class of multiple agent systems (MASs) in the presence of a single high-dimensional leader. Compared with the traditional models for MASs, the inherent dynamics of the leader are allowed to be different with those of the followers in the present framework, which is thus much more favorable in various practical applications. A new kind of distributed controllers associated with a reduced-order state observer are designed for each follower to track the high-dimensional leader under directed switching topology. With the help of M-matrix theory and stability analysis methods of switched systems, some efficient criteria are derived for cooperative consensus tracking of MASs without any external disturbance under directed switching topology. Theoretical analysis is further extended to the case of consensus tracking for MASs subject to unknown external disturbances by showing that, a finite L₂-gain performance for tracking errors against external disturbances can be ensured if some suitable conditions are satisfied. At last, the synthesis issue of designing an observer-based controller to achieve a prescribed L₂-gain performance for consensus tracking is studied by using tools from H control theory, where the underlying topology is assumed to be undirected and fixed. The effectiveness of theoretical results is verified by performing numerical simulations.