Interval Determination for Coefficients of a Characteristic Polynomial in Order to Restrict the Location of the Roots

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Ramezani, Ali Reza | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43499 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Haeri, Mohammad
Abstract:
One of usual criterion which detrimines how much two polynomials are close to each other is smallness of the norm of vector that is formed from subtraction of their corresponding coefficients. Using this criterion, in this dissertation we become involved in investigation of two similar problems. First one is determination of the closest non-Hurwitz polynomial to a Hurwitz one. During this activity, the robustness margin of Hurwitz polynomial whose coefficients are subject to uncertainty is determined. The second problem is determination of the closest Hurwitz polynomial to another polynomial which is not Hurwitz. Unlike to the first problem, this problem is extremely hard. The solution of this problem could be used in design of the internal model controller. We also introduce a usefull tool for examining the effect of uncertainty of coefficients of a polynomial in displacement of the roots from their nominal position.
Keywords:
Internal Model Control (IMC) ; Hurwitz Polynomial ; Robustness Margin ; Uncertainty in Coefficients

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