In this paper, we are concerned with a problem of robust control-oriented system identification in the time domain. Based on the well-known Schur-Takagi-AAK Theorem. we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by-norm. It is also shown that, in the model set defined by the nominal model and the uncertainty bound, there exists at least one model which matches the prescribed input-output data given in the time domain.

This paper investigates estimating the frequency response of the normalized coprime factors of a possibly unstable transfer function from closed-loop frequency domain experimental data. A stochastic framework has been adopted. The dual Youla

This paper deals with probabilistic model set validation. It is assumed that the dynamics of a multi-input multi-output (MIMO) plant is described by a model set with unstructured uncertainties, and identi4cation experiments are performed in closed loop. A necessary and su6cient condition has been derived for the consistency of the model set with both the stabilizing controller and closed-loop frequency domain experimental data (FDED). In this condition, only the Euclidean norm of a complex vector is involved, and this complex vector depends linearly on both the disturbances and the measurement errors. Based on this condition, an analytic formula has been derived for the sample unfalsi4ed probability (SUP) of the model set. Some of the asymptotic statistical properties of the SUP have also been briefly discussed. A numerical example is included to illustrate the e6ciency of the suggested method in model set quality evaluation.

In this paper, the results on the parameterization of all the unfalsified models for single-input/single-output systems are extended to multi-input/multi-output systems. In this arameterization, the assumed a priori plant and noise information are upper bounds of the Hx-norm of the plant matrix-valued transfer function and the noise magnitude. The parameterization is on the basis of several series of plant time-domain identification experiment data. It is shown that for multi-input/multi-output systems, all the unfalsified plant matrix-valued transfer functions can still be expressed by the linear fractional transformation of a fixed matrix-valued transfer function and an Hx-norm bounded structure fixed, but uncertain matrix-valued transfer function. However, the high dimensions of the matrix-valued transfer functions involved in the parameterization hamper the direct application of these results to robust controller design. To overcome these difficulties, further efforts are needed.

Quality assessment is investigated under a probabilistic framework in this note for a prescribed model set. The results on unfalsified probability estimation are extended from additive modeling errors to normalized coprime factor perturbations. An analytic formula has been derived for the sample unfalsified probability. It is shown that with increasing the data length, the sample unfalsified probability converges in probability to a number which is independent of experimental data. Numerical simulations show that the proposed sample unfalsified probability is appropriate in the evaluation of the quality of a model set.