Discrete-time norms of flexible structures

The paper presents and analyses the H2, 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 H2 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 H2 norm does not.