Optimal H/sup ∞/ approximation by systems of prescribed order using frequency response data

Glaum, M.; Lin, Liang Yu; Zames, G.

doi:10.1109/cdc.1996.573119

Cited by 13 publications

(3 citation statements)

References 5 publications

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“…The first is concerned with the effect of the multiplicative noise (9) on the data sequence at Step 1. Proposition 4.1: Let the frequency response measurement samples of the physical plant be given by (9) and the data sequence be constructed as in (12). Then there holds where and We thus obtain, by the hypothesis on the noise sequence Since is arbitrary, the proposition is true.…”

Section: Identification Error Boundsmentioning

confidence: 93%

“…For both and -width defined by (11) can be computed exactly [33], where is the set of trigonometric polynomials of degree no larger than , and is any -dimensional subspace of . The model set has been used extensively for identification in [1], [3], [4], [18], [20], [21], [26], [28], [31], [32], and the set is recently investigated in [12]. Finally, we would like to mention that if one aims at identification of normalized left coprime factors of , the assumption , the number of inputs is larger than or equal to the number of outputs, needs to be imposed for loopshaping purposes.…”

Section: Problem Formulation and Motivationmentioning

confidence: 99%

“…• Step 1: For the frequency response measurement samples in (9), compute the data sequence (12) for , and compute -point inverse discrete Fourier transformation of according to (13) where , and .…”

Section: Proposed Identification Algorithmmentioning

confidence: 99%

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Modeling of normalized coprime factors with ν-metric uncertainty

1999

IEEE Trans. Automat. Contr.

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Modeling of uncertain systems with normalized coprime factor description is investigated where the experimental data is given by a finite set of frequency response measurement samples of the open loop plant that is linear, time-invariant, and possibly infinite-dimensional. The objective is not only to identify the nominal model but also to quantify the modeling error with sup-norm bounds in frequency domain. The uncertainty to be identified and quantified is chosen as the -metric, proposed by Vinnicombe [43], because of its compatibility with H 1 -based robust control. An algorithm is developed to model the normalized coprime factors of the given plant using techniques of discrete Fourier analysis (DFA) and balanced stochastic truncation (BST) and is shown to be robust in the presence of the worst case noise. Upper bounds are derived for the associated modeling error based on the minimum a priori information of the underlying model set and of the noise level in the measurement data. A simulation example is used to illustrate the effectiveness of the proposed algorithm.

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Section: Identification Error Boundsmentioning

confidence: 93%