Formation Design for Third-Order Multi-Agent Systems

This paper establishes a necessary and sufficient condition for designing formation in third-order multi-agent systems which are networked by digraphs. We assume that the control input of each agent is constructed based on weighted difference between its states and those of its neighbor agents, and define the desired time-varying formation with piecewise continuously differentiable vectors. By transforming the formation problem into a consensus problem and using Hurwitz polynomials with complex coefficients, we obtain the necessary and sufficient condition for the multi-agent systems to achieve the desired formation.