Robust $H_\infty$ Estimation of Uncertain Linear Quantum Systems
For researchers working on quantum systems, this provides a robust estimation method that handles uncertainties, though it is an incremental extension of existing H∞ control techniques to a specific class of quantum systems.
The paper develops a robust H∞ estimator for uncertain linear quantum systems, solving the estimation problem by converting it to a scaled H∞ control problem and obtaining solutions via two algebraic Riccati equations. Examples with dynamic squeezers demonstrate the method's efficacy.
We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust $H_\infty$ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled $H_\infty$ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method.