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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 20, 2008
IMA Journal of Mathematical Control and Information 2008 25(4):507-514; doi:10.1093/imamci/dnn009
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Kharitonov theorem with degree drop: the complex case

Onur Toker{dagger}

Department of Electronics Engineering, Fatih University, Buyukcekmece 34500, Istanbul, Turkey

{dagger} Email: onur{at}fatih.edu.tr

Accepted on July 26, 2008

In this paper, we study the complex version of the Kharitonov theorem without the constant-degree assumption. It is proved that, for a complex-interval polynomial with degree drop, robust Hurwitz stability is equivalent to the Hurwitz stability of the eight Kharitonov polynomials. Furthermore, it is also shown that for a robustly stable complex-interval polynomial, degree drop cannot exceed one and degree drop can only occur at one of the corners of the rectangular region in the complex plane corresponding to the leading coefficient of the uncertain polynomial.

Keywords: Kharitonov theorem.


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