Asymptotic stability and bounded-input, bounded-output (BIBO) stability of a class of underdamped mechanical structures with nonlinear time-varying perturbations are studied. An upper norm-bound of the state transition matrix of a normal mode system is derived. We provide a sufficient condition which guarantees both asymptotic stability and BIBO stability for the perturbed system. A straightforward extension to a robust modal-space control is also briefly introduced. Finally, simple illustrative examples are presented for demonstrating the applications of our results

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