Distributed containment of heterogeneous multi-agent systems with switching topologies

In this article, we investigate the issue of containment control for a heterogeneous multi-agent system composed of stationary leaders, first-order dynamic followers and second-order dynamic followers under switching communication topologies. For the followers with different order dynamic behavior, two distributed dynamic state feedback algorithms are constructed separately for the followers driven by different dynamics. To achieve the objective of this work, we convert the heterogeneous containment control problem into a convergence problem, which is the product of time-varying non-negative matrices whose sum of each row is less than or equal to 1. With the aid of the matrix product technique and the composite binary relation, a sufficient condition can be established to analyze the convergence problem. At last, some numerical examples are presented to verify the feasibility of the theoretical findings.