Disturbance observer‐based matrix‐weighted consensus

Abstract

AbstractIn 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.