### Paul Van Dooren

SLICOT Working Note 1999-9: June 1999.

In this note a survey is given of areas of systems and control where structured matrix problems are important. In identification we mention four different types of data collection : impulse response, input-output pairs, frequency response and covariance data. In each of those, the identification problem can be rewritten in terms of structured matrix problems for which there exist fast decompositions. The use of structured matrix decompositions should yield an improvement in speed of computations. In analysis and design one encounters eigenvalue problems with specific structure such as cyclic, Hamiltonian and symplectic matrices. For those problems it is important to use structure preserving decompositions, mainly to improve the numerical accuracy of the computations, although these algorithms typically yield improved computational complexities as well. We also list the key numerical routines that should be provided in the SLICOT library in order to tackle most of the problems mentioned in this note.