Practical synchronization of discrete-time multi-agent systems under finite input sets

In this paper, we study the coordination of discrete-time multi-agent systems under finite input sets. For uniformly quantized finite input sets, we design admissible control protocols based on relative state feedback and finite-level uniform quantization scheme to ensure practical synchronization. It is shown that the coarseness of the input set being less than an upper-bound depending on the network topology and the given synchronization precision is necessary and sufficient for the existence of admissible control protocols under which the system can achieve practical synchronization in some sense. This result builds a bidirectional relationship between the coarseness of the input set and the synchronization precision, and also gives the coarsest condition on the input set that enables the system to achieve synchronization under given precision.