Whidborne, James F.Gu, Da-WeiWu, JunChen, Sheng2011-11-132011-11-132005-06-01James F. Whidborne, Da-Wei Gu, Jun Wu, Sheng Chen. Optimal Controller and Filter Realisations using Finite-precision, Floating-point Arithmetic. International Journal of Systems Science. 10 June, 2005, Vol 36 Iss 7, p405-4130020-7721http://dx.doi.org/10.1080/00207720500148378http://dspace.lib.cranfield.ac.uk/handle/1826/1234The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered. Floating-point arithmetic parameter uncertainty is multiplicative, unlike parameter uncertainty resulting from fixed-point arithmetic. Based on first- order eigenvalue sensitivity analysis, an upper bound on the eigenvalue perturbations is derived. Consequently, open-loop and closed-loop eigenvalue sensitivity measures are proposed. These measures are dependent upon the filter/ controller realization. Problems of obtaining the optimal realization with respect to both the open-loop and the closed-loop eigenvalue sensitivity measures are posed. The problem for the open-loop case is completely solved. Solutions for the closed-loop case are obtained using non-linear programming. The problems are illustrated with a numerical example.This is a preprint of an article whose final and definitive form has been published in the International Journal of Systems Science (C)2005 Taylor & Francis; International Journal of Systems Science is available online at: http://www.informaworld.com/ DOI: 10.1080/00207720500148378Finite-precision arithmeticFinite word lengthDigital controllerDigital filterEigenvalue sensitivityFloating-point arithmeticController fragilityArticle