Containment Control of Second-Order Multi-Agent Systems Via Sampled-Data Control

The containment control problem of second-order multi-agent systems in sampled-data setting is investigated in this paper. Based on $M$-matrix theory and the properties of the product of infinite matrices, we first transform the containment control problem into an asymptotically stabilization problem, which is equivalent to designing a Schur polynomial with complex coefficients. Then, we obtain a necessary and sufficient condition by performing a bilinear transformation between Schur polynomials and Hurwitz polynomials with complex coefficients. Finally, numerical examples are presented to demonstrate the validity of the theoretical findings.

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