Cooperative control with general linear dynamics and limited communication: Periodic updates

This paper studies the consensus problem for a team of agents with general linear dynamics, under directed communication graphs, and subject to limited communication. Transmission of information is not assumed to occur continuously but only at discrete time instants. By assuming a periodic information transmission, two control approaches are proposed. In the first approach a control algorithm is designed for each agent based on models of decoupled dynamics of itself and its neighbors. In the second approach each agent uses Zero-Order-Hold models of the same subset of agents. For both approaches, based on the structure of the communication topology, necessary and sufficient conditions for asymptotic consensus are provided. These conditions define the range of periods that can be implemented. Sufficient conditions are also derived which only require an estimate of the spectral radius of the graph Laplacian.