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New unbiased H infinity functional filters designs for discrete‐time linear systems Time and frequency domains approaches

New unbiased H infinity functional filters designs for discrete‐time linear systems Time and... Purpose – The purpose of this paper is to propose solutions for both discrete‐time and frequency‐domain designs of unbiased H ∞ functional filters for discrete‐time linear systems affected by bounded norm energy disturbances. Design/methodology/approach – The discrete‐time procedure design is based on the unbiasedness of the functional filter using a Sylvester equation; then the problem is expressed in a singular system one and is solved in terms of linear matrix inequalities (LMIs). The frequency procedure design is derived from discrete‐time domain results by defining some useful matrix fraction descriptions and mainly, establishing the useful and equivalent form of the connecting relationship that parameterizes the dynamics behavior between discrete‐time and z‐domain. Findings – The performance of the proposed approach is illustrated with the aid of a practical example. The proposed methods are easily implementable and concern a more general class of systems, as the transformation of the system in a singular one permits to treat the problem of perturbance advanced. Originality/value – First, the order of this filter is equal to the dimension of the vector to be estimated, which is benefit in case of control purpose (reduction of time calculation comparing to the full order one). Second, all recent works on the functional filtering consider systems which permit to avoid to have advanced perturbation term in the error dynamics; the authors propose here an approach which resolves the H ∞ filtering problem even when the term is present. In addition, it permit to consider more general class of discrete‐time systems. Furthermore, the LMI approaching the discrete‐time case permits to handle with more general problem ( H ∞ , L 2 − H ∞ ) than the classical Riccati one. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Intelligent Computing and Cybernetics Emerald Publishing

New unbiased H infinity functional filters designs for discrete‐time linear systems Time and frequency domains approaches

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Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
1756-378X
DOI
10.1108/17563781111160048
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to propose solutions for both discrete‐time and frequency‐domain designs of unbiased H ∞ functional filters for discrete‐time linear systems affected by bounded norm energy disturbances. Design/methodology/approach – The discrete‐time procedure design is based on the unbiasedness of the functional filter using a Sylvester equation; then the problem is expressed in a singular system one and is solved in terms of linear matrix inequalities (LMIs). The frequency procedure design is derived from discrete‐time domain results by defining some useful matrix fraction descriptions and mainly, establishing the useful and equivalent form of the connecting relationship that parameterizes the dynamics behavior between discrete‐time and z‐domain. Findings – The performance of the proposed approach is illustrated with the aid of a practical example. The proposed methods are easily implementable and concern a more general class of systems, as the transformation of the system in a singular one permits to treat the problem of perturbance advanced. Originality/value – First, the order of this filter is equal to the dimension of the vector to be estimated, which is benefit in case of control purpose (reduction of time calculation comparing to the full order one). Second, all recent works on the functional filtering consider systems which permit to avoid to have advanced perturbation term in the error dynamics; the authors propose here an approach which resolves the H ∞ filtering problem even when the term is present. In addition, it permit to consider more general class of discrete‐time systems. Furthermore, the LMI approaching the discrete‐time case permits to handle with more general problem ( H ∞ , L 2 − H ∞ ) than the classical Riccati one.

Journal

International Journal of Intelligent Computing and CyberneticsEmerald Publishing

Published: Aug 23, 2011

Keywords: Discrete‐time domain; Frequency domain; Linear system; Unbiased H ∞ filtering; Linear matrix inequalities; Matrix fractions; Design; Control systems

References