The robust distributed estimation for a class of time-invariant plants is achieved via a finite-time observer, its error reaching zero after a finite time in the absence of perturbation. Two types of robustness are also shown. First, input-to-state stability with respect to measurement noises and additive perturbations is proven. Second, we demonstrate that the estimation error stays bounded in the presence of known transmission delays.

A design of a distributed observer is proposed for continuous-time systems with nonlinear observer nodes such that the estimation errors converge in a finite time to zero. By taking advantage of individual observability decompositions, the designs for the locally observable and the unobservable substate are made independent from each other. For the observable substate of each node, standard centralized finite-time observer techniques are applied. To estimate distributively the unobservable substate, the observer nodes employ consensus coupling in a linear term and an additional term embedded in a fractional power. The approach is derived using homogeneity arguments and it leads to a simple design with an LMI that is guaranteed to be feasible under general conditions.