Robust Stability and Performance Analysis of Quantum Systems

Abstract

This chapter presents several results on robust stabilityRobust stability and performance analysisPerformance analysis for uncertain quantum systems using the small gain theoremSmall gain theorem and a Popov approachPopov approach. In Sect. 7.2, the problem of robust stability for linear quantum systems is presented. Section 7.3 discusses the robust stability of several classes of nonlinear quantum systems including cases with non-quadratic Hamiltonian perturbations, uncertainties in nonlinear coupling operators and nonlinear dynamic uncertainties. In Sect. 7.4, performance analysis and guaranteed cost control are investigated for uncertain linear quantum systems $$^\text {a}$$ . Section 7.5 presents several results on performance analysis for nonlinear quantum systems.