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The paper presents and analyses the H 2 , H ∞ , and Hankel norms of flexible structures. The analysis is conducted for the discrete-time models of structures and compared with the continuous-time results. The structural state-space models are presented in modal co-ordinates. Closed-form expressions for norms of structural modes are obtained, and norms of a structure are determined from the modal norms. The relationships between the Hankel, H ∞ , and H 2 modal norms are derived. In addition, the paper shows that the discrete-time Hankel and H ∞ norms converge to the continuous-time counterparts when the sampling time approaches zero; however, the H 2 norm does not. |
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