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Journal of Applied Mathematics
Volume 2012, Article ID 840603, 32 pages
Research Article

Interval Continuous Plant Identification from Value Sets

1Departamento de Sistemas de Comunicación y Control, UNED, c/Juan del Rosal 16, 28040 Madrid, Spain
2Departamento de Tecnología de Computadores y Comunicaciones, Universidad de Extremadura, 06800 Madrid, Spain

Received 13 April 2012; Revised 1 September 2012; Accepted 1 September 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 R. Hernández et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper shows how to obtain the values of the numerator and denominator Kharitonov polynomials of an interval plant from its value set at a given frequency. Moreover, it is proven that given a value set, all the assigned polynomials of the vertices can be determined if and only if there is a complete edge or a complete arc lying on a quadrant. This algorithm is nonconservative in the sense that if the value-set boundary of an interval plant is exactly known, and particularly its vertices, then the Kharitonov rectangles are exactly those used to obtain these value sets.