Abstract
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.
Highlights
In reference to the identification problem, these have been widely motivated and analysed over recent years 1
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
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
Summary
In reference to the identification problem, these have been widely motivated and analysed over recent years 1. A different approach was developed by Hernandez et al 10 studying the problem from the extreme point results point of view This was a first step for the identification of an interval plant, showing three main properties to characterize the value set lying on a quadrant. This paper improves the results obtained in 10 and shows how to obtain the values of the numerator and denominator Kharitonov polynomials when the value sets have less than five vertices in the same quadrant. Identification with such an interval plant allows engineers predict the worst case performance and stability margins using the results on interval systems, extreme point results
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