This paper discusses optimal Hankel norm approximations (HNA) of continuous-time descriptor systems. The main results are based on the fact that the system can be decomposed into a slow subsystem and a fast subsystem. We mainly stress the reduction for the subsystems. In this sense, the novelty is two-fold. First, by exploring the structure of the Hankel matrix associated with the fast subsystem, a connection between reachability, observability and the system index is discovered. Second, an index reduction technique is proposed by reducing the system in the optimal Hankel norm manner. Numerical examples are tested to demonstrate the theoretical aspects of the article.
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