A coupled pair of Luenberger observers for linear systems to improve rate of convergence and robustness to measurement noise

Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems that consists of the combination of two coupled Luenberger observers. The output of the proposed observer is defined as the average between the estimates of the individual ones. The convergence rate and the robustness to measurement noise of the proposed observer's output are characterized in terms of ISS estimates. Conditions guaranteeing that these estimates outperform those obtained with a standard Luenberger observer are given. The conditions are exercised in a stable scalar plant, for which a design procedure and numerical analysis are provided, and in a second order plant, numerically.