  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.
