Modified fast-sample/fast-hold approximation and γ-independent H∞-discretisation for general sampled-data systems by fast-lifting

Authors: Hagiwara, Tomomichi; Okada, Koichiro

Source: International Journal of Control, Volume 82, Number 9, September 2009 , pp. 1762-1771(10)

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Abstract:

This article is concerned with the fast-lifting approach to H∞ analysis and design of sampled-data systems, and extends our preceding study on modified fast-sample/fast-hold (FSFH) approximation, in which the direct feedthrough matrix D11 from the disturbance w to the controlled output z was assumed to be zero. More precisely, this article removes this assumption and shows that a γ-independent H∞ discretisation is still possible in a nontrivial fashion by applying what we call quasi-finite-rank approximation of an infinite-rank operator and then the loop-shifting technique. As in the case of D11 = 0, the modified FSFH approach retains the feature that both the upper and lower bounds of the H∞-norm or the frequency response gain can be computed, where the gap between the upper and lower bounds can be bounded with the approximation parameter N and is independent of the discrete-time controller. This feature is significant in applying the new method especially to control system design, and this study indeed has a very close relationship to the recent progress in the study of control system analysis/design via noncausal linear periodically time-varying scaling. The significance of a key lemma pertinent to the fast-lifting approach is suggested in connection with such a relationship, and also with its application to time-delay systems.

Keywords: fast-lifting; H∞ discretisation; quasi-finite-rank approximation; loop-shifting

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00207170902748732

Affiliations: 1: Department of Electrical Engineering, Kyoto University, Kyoto 615-8510, Japan

Publication date: 2009-09-01

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