Title: A Survey of Riccati Equation Results in Negative Imaginary Systems Theory and Quantum Control Theory,
Abstract: This paper presents a survey of some new applications of algebraic Riccati
equations. In particular, the paper surveys some recent results on the use of
algebraic Riccati equations in testing whether a system is negative imaginary
and in synthesizing state feedback controllers which make the closed loop
system negative imaginary. The paper also surveys the use of Riccati equation
methods in the control of quantum linear systems including coherent $H^\infty$
control.