A Survey of Riccati Equation Results in Negative Imaginary Systems Theory and Quantum Control Theory

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∞ control.This work was supported by the Australian Research Council (ARC) under grants FL110100020 and DP160101121 and the Air Force Office of Scientific Research (AFOSR), under agreement number FA2386-16-1-4065