On the Lack of Robustness of Observers for Systems with Uncertain, Unstable Dynamics.

We consider the robustness of state estimation for linear, time-invariant systems. Since state estimation is dual to full-state feedback, it may be expected that stability of the error dynamics depends continuously on perturbations of the dynamics matrix. This paper shows, however, that, if the system dynamics are unstable, then—regardless of how the filter gain is chosen—there always exist arbitrarily small perturbations of the system dynamics that give rise to unbounded state-estimation error. Since this phenomenon cannot occur in full-state feedback control, this result reveals a surprising break-down in the duality between estimation and control.