Leader-following consensus for linear discrete-time multi-agent systems subject to static networks

The leader-following consensus problem for linear discrete-time multi-agent systems subject to static networks has been studied in the literature using H∞ Riccati inequality design and H2 Riccati equation design, respectively. However, these methods involve some less tractable conditions and need to solve some type of Riccati equation or inequality. In this paper, we further study the leader-following consensus problem for linear discrete-time multi-agent systems subject to static networks for the case where the leader system is marginally stable. By showing the Schur stability of some graph matrix, which can be viewed as the discrete-time counterpart of H matrix encountered in continuous-time leader-following consensus problem, we solve our problem with a straightforward method, which is the reminiscent of the same problem for continuous-time multi-agent systems.

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