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• W4377710191 abstract "The generalization of the Routh stability test to the corresponding zero location problem of determining how many of the zeros of a polynomial have negative real parts, positive real parts, or are purely imaginary encountered intensive and controversial activity about overcoming singular cases. This paper revisits this problem and presents two (MaxQ and LinQ) ZL methods for an arbitrary complex polynomial. The first method produces for an investigated polynomial <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$P(s)$ </tex-math></inline-formula> of degree <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$n$ </tex-math></inline-formula> a sequence of length <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$leq n+1$ </tex-math></inline-formula> of para-even or para-odd (para-paritic) polynomials of descending degrees obtained by a polynomial remainder routine with quotients of <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>maximal</i> degrees. The second method uses successively <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>linear</i> quotients for the reduction of degrees and thus assign to <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$P(s)$ </tex-math></inline-formula> always a sequence of exactly <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$n+1$ </tex-math></inline-formula> para-paritic polynomials. Previous so-called first-type singularities become “non-essential singularities” in the sense that they are now absorbed into modified forms of the polynomial recursions. The distribution of zeros with respect to the imaginary axis is extracted in both methods by sign variation rules posed on the leading coefficients (that stay real when testing a complex polynomial as well) of the polynomials in the sequence." @default.
• W4377710191 created "2023-05-24" @default.
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• W4377710191 date "2023-07-01" @default.
• W4377710191 modified "2023-09-27" @default.
• W4377710191 title "Routh Zero Location Tests Unhampered by Nonessential Singularities" @default.
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• W4377710191 doi "https://doi.org/10.1109/tcsi.2023.3272638" @default.
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