Performance Analysis and Coherent Guaranteed Cost Control for Uncertain Quantum Systems Using Small Gain and Popov Methods

TL;DR

This paper applies small gain and Popov methods to analyze and control uncertain quantum systems, demonstrating improved performance and less conservatism in control design through coherent guaranteed cost controllers.

Contribution

It extends quantum small gain and Popov methods to performance analysis and designs less conservative controllers for uncertain quantum systems.

Findings

Popov method yields less conservative results than small gain.

Coherent guaranteed cost controllers improve system performance.

Illustrative example validates theoretical approaches.

Abstract

This paper extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear quantum system and is subject to quadratic perturbations in the system Hamiltonian. Based on these two methods, coherent guaranteed cost controllers are designed for a given quantum system to achieve improved control performance. An illustrative example also shows that the quantum Popov approach can obtain less conservative results than the quantum small gain approach for the same uncertain quantum system.