Discrete-time frequency weighted model reduction and application to sampled-data models

The problem of frequency weighted optimal model order reduction for discrete-time systems is considered. Necessary conditions which completely characterize the reduced-order model are given. The solution of the problem consists of a set of one generalized Riccati equation and two generalized Lyapunov equations all coupled by a projection. The results that were obtained for this problem are used to solve the problem of finding the optimal, fixed-order, discrete-time model for a sampled-data continuous-time system. Several configurations and cost functions, each corresponding to a certain physical scenario, are considered.