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

Author

Zhang, Guofeng ; James, Matthew R.

Author_Institution

Dept. of Appl. Math., Hong Kong Polytech. Univ., Hong Kong, China

Volume

56

Issue

7

fYear

2011

fDate

7/1/2011 12:00:00 AM

Firstpage

1535

Lastpage

1550

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^∞ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.

Keywords

H^∞ control; Lyapunov matrix equations; control system synthesis; feedback; linear matrix inequalities; linear quadratic Gaussian control; linear systems; optimisation; stability; stochastic systems; LMI; LQG synthesis method; coherent H^∞ synthesis; coherent feedback control; complex Lyapunov equation; direct coupling design; dissipation; indirect coupling design; linear matrix inequalities; linear quantum stochastic system; multistep optimization; stability; Couplings; Equations; Feedback control; Mathematical model; Oscillators; Quantum mechanics; Stability analysis; $H^{infty}$ control; Coherent feedback; LQG control; dissipation; gain; passivity; quantum feedback control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2096010

Filename

5648449