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A method to quantify robust performance for situations where structuredparameter variations and initial state errors rather than extraneousdisturbances are the main performance limiting factors is presented. Theapproach is based on the error dynamics, the difference between nominal andperturbed dynamics, driven by either the unperturbed or perturbed state, ratherthan an artificially imposed disturbance. The unperturbed versus perturbeddichotomy can be interpreted as the relative error dynamics scaled by eitherthe unperturbed or perturbed dynamics. The error dynamics driven by unperturbedstate has the unique feature of decoupling the effect of physically meaningfuluncertainties from an additive disturbance. The perturbed case offers thepossibility to side-step Structured Singular Value (SSV) computations.Applications to a lightly damped mechanical system and a slowly dephasingquantum system demonstrate the usefulness of the concepts across a broad rangeof systems. Finally, a fixed-point algorithm specifically developed for quantumsystems with state transitions depending in a nonlinear fashion onuncertainties is proposed as the substitute for classical SSV.

Disturbance-agnostic robust performance with structured uncertainties and initial state error in classical versus quantum oscillatory systems