Convergence rates are analyzed for Recursive Prediction (Output) Error Methods (RPEM) in the identification of linear state-space systems from (noisy) impulse response data) RPEM algorithms are derived which are suitable for the identification of the parameters in arbitrary state-space structures. Deterministic and stochastic versions of these identification algorithms are presented. These two classes indicate the number of realizations used in the identification, not the presence or absence of noise. The convergence analysis uses the eigen-information of the correlation matrix (really its inverse, the Fisher information matrix) for a chosen parameterization. This analysis explains why various state-space structures have different convergence properties, 1.e., why for the same system the estimation processes corresponding to different identification structures converge at different rates. The eigen-information of the parameter information matrix relates the system sensitivity and numerical conditioning in a manner which provides insight into the identification process. The relevant eigen-information is combined in the proposed scalar convergence time constant +. One important result is that identification of the usually identified direct form II parameters (the standard ARMA parameters) does not necessarily yield the fastest parameter set convergence for the system being identified. Identification from arbitrary input is also briefly considered, as is identification when the model order is different from the “true” system order. / Ph. D.

The convergence rates for the method of Weinstein and a variant method of Aronszajn known as "truncation including the remainder" are derived in terms of the containment gaps between exact and approximating subspaces, using analytical techniques that arise in part in the convergence analysis of finite element methods for differential eigenvalue problems. An example of a one dimensional Schrodinger operator with a potential is presented which arises in quantum mechanics. Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch are considered. Since the EVF method uses finite element trial functions as approximating vectors, it produces sparse and well-structured coefficient matrices. For these large-order sparse matrix eigenvalue problems, we adapt a spectral transformation Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples of vibration in beams and plates, convergence behavior is experimentally evaluated. / Ph. D.