Comments on "Comments on the Routh - Hurwitz criterion

Khatwani, K.

doi:10.1109/tac.1981.1102675

IEEE Trans. Automat. Contr.

1981

DOI: 10.1109/tac.1981.1102675

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Comments on "Comments on the Routh - Hurwitz criterion

K. Khatwani

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A novel approach for root distribution analysis of linear time‐invariant systems using Routh and Fuller tables

Sivanandam¹,

Deepa²

2009

Asian Journal of Control

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The root distribution of a given characteristic equation of a linear time‐invariant system can be analyzed with the help of a Routh table using the elements of the first column in the table. In the case of unstable systems, sometimes, a zero element may appear in the third row of the first column of the Routh array. This prematurity can be suitably handled as indicated by various authors. In this paper, the given characteristic polynomial having roots in the right hand plane is multiplied by a suitable polynomial, and Routh and Fuller tables are applied for the resultant polynomial to infer the complete root distribution. Further, the column polynomials from each table are adopted to know more about root distribution, which forms the core of the proposed work. The Routh table helps in counting and locating roots in the s‐plane, and the Fuller table helps in depicting whether the roots are distinct or complex in nature. In this regard, it is shown in this paper that the simultaneous integration of Routh and Fuller tables yields a good amount of information regarding the root distribution in the s‐plane. The newly presented procedure is illustrated with examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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A novel approach for root distribution analysis of linear time‐invariant systems using Routh and Fuller tables

Sivanandam¹,

Deepa²

2009

Asian Journal of Control

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Extended table for eliminating the singularities in Routh's array

Benidir

Picinbono

1990

IEEE Trans. Automat. Contr.

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Absfmcf-A simple procedure for eliminating the classical E-method introduced by the Routh-Hunvitz test is introduced. This procedure extends the construction of the Routh's taMe in the special case of vanishing leading array elements without introducing complementary multiplications. It is shown that it is always possible to associate to any polynomialg an extended Routh's table and the number of sign changes in the first column of this taMe equals the number of zeros of g with positive real part. Generalization of the Hermite-Biehler Theorem and Applications Consequently, when x decreases from +x to-x, the variation of a(x) is given by Finally, as 6a = 6011 + 6012, we obtain from (A-8), (A-9), (A-14) I ~ = 2 m-(G)-p .

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Routh-Hurwitz test under vanishing leading array elements

Yeung

1983

IEEE Trans. Automat. Contr.

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Comments on "Comments on the Routh - Hurwitz criterion

Cited by 4 publications

References 1 publication

A novel approach for root distribution analysis of linear time‐invariant systems using Routh and Fuller tables

A novel approach for root distribution analysis of linear time‐invariant systems using Routh and Fuller tables

Extended table for eliminating the singularities in Routh's array

Routh-Hurwitz test under vanishing leading array elements

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