A Survey of Riccati Equation Results in Negative Imaginary Systems Theory and Quantum Control Theory
It provides a consolidated overview for researchers in control theory, but is purely a survey without new results.
This survey reviews recent applications of algebraic Riccati equations in negative imaginary systems theory and quantum control, including testing negative imaginary properties and synthesizing state feedback controllers, as well as coherent H∞ control for quantum linear systems.
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.