In this paper, we investigate the structure of the transfer function set which includes all eliminate the transfer functions deduced from the plant available information. It is shown that when an upper bound of the plant transfer function's H∞-norm has been supplied, and the noise contaminating the time domain identification experiment data is not too significant, such a transfer function set can be parameterized by a linear fractional transformation of two transfer function matrices. One of them is a fixed transfer function matrix which is completely determined by the plant available information and the noise magnitude. The other is a norm bounded, structure fixed, free transfer function matrix. Moreover, it is shown that the problem of analytically obtaining the fixed complexity nominal model that best approximates this transfer function set is as difficult as the μ-synthesis problem.

This paper deals with the problem of estimating the probability under which a model set is not falsified by a set of measured plant frequency response samples. A definition of sample unfalsified probability has been proposed, and an explicit formula has been derived. Computation issues are also discussed. Moreover, an ecient algorithm has been developed for sample unfalsified probability calculation. Monte Carlo simulations show that the defined sample unfalsi-fied probability is appropriate in the evaluation of the quality of a model set. Compared with the deterministic approach, simulation results suggest that the probabilistic approach is more suitable in model set validation.

This paper deals with the problem of obtaining a plant nominal model and its error uncertainty bound when a batch of plant models is provided. While the selection of model set structure is essential and probably depends on the model intended application, in this paper it is assumed that a nominal model is perturbed by its error through a homographic transformation. A necessary and sufficient condition is obtained for a nominal model to be suboptimal. Moreover, an algorithm is proposed to obtain a nominal model which is suboptimal and has a low complexity. Furthermore, the extraction of structured nominal model errors is discussed. The efficiency of the proposed model set determination algorithm is verified through the application to the simultaneous spiral control of two compact disc players.

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.

The problem of parameterizing all unfalsified plant models from closed-loop time-domain dentification experimental data is investigated in this paper. The assumed a priori plant nformation is an upper bound of the Lx norm and the number of the unstable poles of its transfer function. Moreover, it is assumed that magnitude bounds of the disturbances that perturb the closed-loop system have been supplied. Under the condition that the stabilizing controller is known, it is shown that all the unfalsified plant transfer functions can be parameterized by a linear fractional transformation of a fixed transfer-function matrix and an Lx-norm-bounded, structure-fixed but uncertain transfer-function matrix. These results are very similar to those when plant open-loop time-domain identification experimental data are supplied. However, further efforts are still needed in order to apply these results to robust controller design. This results mainly from the computational omplexity and the high dimensions of the transfer-function matrices involved in the arameterization.