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A new general Routh-like algorithm to determine the number of RHP roots of a real or complex polynomial

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1 Author(s)
Agashe, S. ; Indian Institute of Technology, Bombay, India

A new Routh-like algorithm for determining the number of right-half plane (RHP) roots of a polynomial with real or complex coefficients is given. It includes the Routh algorithm for real polynomials as a special case. Moreover, the algorithm also applies directly to the singular case wherein the leading coefficient of a row, but not the entire row, vanishes, needing far fewer computations than the heuristic \epsilon - method about which there was a vigorous discussion in these TRANSACTIONS a few years ago, and further not requiring investigation of an auxiliary polynomial. The algorithm is illustrated by a few examples. The proof of the algorithm is based on the Principle of the Argument, and thus also constitutes a simple proof of the Routh algorithm in the regular case.

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Automatic Control, IEEE Transactions on  (Volume:30 ,  Issue: 4 )