Coherent robust [formula omitted] control of uncertain linear quantum systems with direct and indirect couplings

Abstract

In this paper, a robust H∞ analysis method is presented for a class of uncertain quantum systems where uncertainties may exist in the system and interaction Hamiltonians, and the coupling operators. We provide a sufficient condition to guarantee this class of uncertain systems robust strictly bounded real with respect to a given disturbance attenuation. Moreover, we propose a robust H∞ control method for quantum systems with uncertain system Hamiltonian and uncertain coupling operators. The controller and the quantum plant are connected via direct and indirect couplings. This robust H∞ control problem is shown to have a connection with a scaled H∞ problem. We propose a numerical procedure to find the corresponding coefficients of the desired H∞ controller by using an LMI formulation and multi-step optimization.