Design of coherent quantum observers in the presence of unknown inputs

In this paper, we proceed with our research on coherent quantum observers, with a focus on the scenario where there exist unknown inputs to the quantum plant. In our previous studies, we were mainly concerned with linear quantum plants in the absence of unknown inputs. However, when there are unmodeled dynamics or disturbances in quantum systems, the quantum version of Luenberger observers or Kalman filters might not be adequate. Given that no prior knowledge is assumed for the unknown inputs, we take advantage of the Hautus lemma to improve the robustness in observing a quantum system. More precisely, we consider linear quantum stochastic systems with unknown inputs involved whose dynamics correspond to open quantum harmonic oscillators. We show the procedure regarding synthesis of coherent observers for such systems that accomplish the task of simultaneously estimating system variables together with the unknown inputs, which is also illustrated by a simulation example.