On Stability of Consensus Control of Discrete-Time Multi-Agent Systems by Multiple Pinning Agents

In this letter, we consider the consensus problem of discrete-time multi-agent systems where all states of all agents converge to a desired state by pinning multiple agents with state feedback controllers. By using the Gershgorin Theorem, we show sufficient conditions such that one of root loci of the multi-agent system crosses the unit circle earliest along the real axis and then diverges to minus infinity as the pinning gain increases from 0 to infinity, thus the upper bound of the pinning gain that achieves the consensus is obtained.