Disturbance observer-based matrix-weighted consensus

In this paper, we proposed several disturbance observer-based matrix-weighted consensus algorithms. A new disturbance observer is firstly designed for linear systems with unknown matched or mismatched disturbances representable as the multiplication of a known time-varying matrix with a unknown constant vector. Under some assumptions on the boundedness and persistent excitation of the regression matrix, the disturbances can be estimated at an exponential rate. Then, a suitable compensation input is provided to compensate the unknown disturbances. Second, disturbance-observer based consensus algorithms are proposed for matrix-weighted networks of single- and double-integrators with matched or mismatched disturbances. We show that both matched and mismatched disturbances can be estimated and actively compensated, and the consensus system uniformly globally asymptotically converges to a fixed point in the kernel of the matrix-weighted Laplacian. Depending on the network connectivity, the system can asymptotically achieve a consensus or a cluster configuration. The disturbance-observer based consensus design is further extended for a network of higher-order integrators subjected to disturbances. Finally, simulation results are provided to support the mathematical analysis.