We propose a protocol to solve the leader-following consensus problem in discrete-time under a fixed and time-invariant communication topology. Each agent is composed of general linear dynamics and is assumed to be homogeneous. While much of the literature obtains a bound of the fixed coupling gain in the continuous-time scenario, we illustrate there exists a different converging condition in discrete-time under an undirected communication topology. A novel distributed adaptive controller is also introduced, which only depends on the estimated bound of the maximum eigenvalue of the Laplacian matrix and the state estimates received from the agent's neighbours. The analysis is further extended to the case of heterogeneous agents without uncertainty. It is shown that the consensu...[ Read more ]

We propose a protocol to solve the leader-following consensus problem in discrete-time under a fixed and time-invariant communication topology. Each agent is composed of general linear dynamics and is assumed to be homogeneous. While much of the literature obtains a bound of the fixed coupling gain in the continuous-time scenario, we illustrate there exists a different converging condition in discrete-time under an undirected communication topology. A novel distributed adaptive controller is also introduced, which only depends on the estimated bound of the maximum eigenvalue of the Laplacian matrix and the state estimates received from the agent's neighbours. The analysis is further extended to the case of heterogeneous agents without uncertainty. It is shown that the consensus error and tracking error can both be minimized with additional integrator dynamics.