A new majorant robustness analysis test that yields frequency-dependent performance bounds for closed-loop uncertain vibrational systems with frequency, damping and mode shape uncertainty is developed. Specifically, for closed-loop systems consisting of uncertain positive real plants in tandem with sensor and actuator dynamics and controlled by strictly positive real compensators, performance bounds are developed by decomposing the equivalent compensator (which includes the actuator and sensor dynamics) into a generalized positive real part and a non-generalized positive real part, and by using concepts of M-matrices and majorant analysis.