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

TL;DR

This survey reviews recent advances in algebraic Riccati equations applied to negative imaginary systems and quantum control, highlighting new methods for system analysis and controller synthesis.

Contribution

It compiles and discusses recent results on Riccati equations in negative imaginary systems and quantum control, emphasizing new applications and techniques.

Findings

Riccati equations are effective in testing negative imaginary properties.

New controller synthesis methods for negative imaginary systems are surveyed.

Applications to quantum linear systems and coherent H-infinity control are included.

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.