Convergence Rate Analysis of Multi-Agent Positive Systems under Formation Control: An Efficient Algorithm by Exploiting Positivity

This paper is concerned with convergence rate analysis of multi-agent positive systems under formation control. Recently, we have shown that very basic multi-agent systems under formation control can be modeled as interconnected positive systems, and desired formation can be achieved by designing interconnection matrices appropriately. In such formation control, the resulting convergence performance (i.e., convergence rate) varies according to the interconnection matrices and this fact motivates us to develop an efficient algorithm for the analysis of the convergence rate. In this paper, assuming that the dynamics of agents are positive and homogeneous, we conceive such an algorithm by problem decomposition. We show that the decomposition to smaller size problems and drastic reduction of computational burden become possible by making full use of the positivity of the agents.