Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

TL;DR

This paper develops methods for designing direct and indirect couplings in coherent feedback control of linear quantum systems, ensuring stability and performance using Lyapunov equations and LMIs.

Contribution

It introduces a general physical model for coupled linear quantum systems and extends $H^$ and LQG synthesis to include direct couplings.

Findings

Characterization of stability, dissipation, passivity, and gain properties.

Extension of coherent $H^$ and LQG synthesis methods to direct couplings.

Illustrative examples demonstrating the design procedures.

Abstract

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.