Robust distributed state observers with performance guarantees and optimized communication graph

Motivated by the design of observers with good performance and robustness, the problem of estimating the state of a linear time-invariant plant in a distributed fashion, over a graph, is considered. By attaching to each node a linear observer and defining an innovation term that employs information received from neighbors, we propose a distributed state observer that satisfies a pre-specified rate of convergence and has optimized robustness to measurement noise. The convergence rate and the robustness to measurement noise of the proposed observer are characterized in terms of KL bounds as well as in terms of (nonlinear and linear) optimization problems. Moreover, conditions on the plant for which the proposed observer has an H_∞ gain from noise to local estimate that is smaller than that of a single Luenberger observer is given. The properties of the proposed distributed state observer are shown analytically and validated numerically.