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.

A shortened version of this paper will appear in the Proceedings of the 20th IFAC World Congress

References in corpus (7)

• Coherent quantum LQG control
• Coherent-feedback quantum control with a dynamic compensator
• Linear Quantum Feedback Networks
• Avoiding entanglement sudden-death via measurement feedback control in a quantum network
• Robust Stability of Uncertain Quantum Systems
• Physical Realizability of Multi-Level Quantum Systems
• Feedback Control of Negative-Imaginary Systems: Large Flexible structures with colocated actuators and sensors