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This paper derives a subspace identification algorithm for a δ-operator state-space model by using the methods due to Moonen et al. [11], [12], [21]. Since the δ-operator model converges to a continuous-time model as the sampling interval goes to zero, the algorithm obtained is applicable to the identification of continuous-time medels. A method of computing the state vector from the block Hankel matrix is developed. Simulation studies show the present algorithm provides good results for the case of a low N/S ratio. Improvement of the algorithm for the case of a higher N/S ratio remains to be done.

This paper considers the H∞ estimation problem by using a model matching technique. For a given possibly unstable plant, the H∞ estimation problem is reduced to a standard model matching problem by introducing a class of all stable and unbiased estimators. Based on Nehari's theorem, a necessary and suffcient condition for the existence of a solution of the H∞ estimation problem is derived in terms of an H∞-type algebraic Riccati equation. The LFT representation of the class of all solutions is also developed.

This paper derives the solutions to the Wiener filtering and stationary LQG problem for a discrete-time system by applying the state-space techniques developed for H₂, H∞ optimal controls. As mathematical preliminaries, we collect useful operations for the transfer function matrices. We also provide a new proof for the inner-outer factorization algorithm that appears in the discrete-time H₂ optimization.

This paper derives solutions to the multivariable Wiener filtering and the stationary LQG problems using the H₂ optimal control theory and the state-space technique. Inner-outer factorization and spectral factorization results arising in H₂/H∞ optimal controls are also derived by the state-space technique.