Title: A computationally faster algorithm to test the stability of characteristic polynomials

Authors: Panneerselvam Kavitha; Ayyagari Ramakalyan

Addresses: Department of Instrumentation and Control Engineering, National Institute of Technology, Tamilnadu, Tiruchirappalli, 620012, India ' Department of Instrumentation and Control Engineering, National Institute of Technology, Tamilnadu, Tiruchirappalli, 620012, India

Abstract: In system theory and control, stability of a given system is an important specification; often we design controllers with stability as the highest priority. It was James Maxwell in 1867, who first showed that an examination of the coefficients of differential equations governing the system, would reveal the stability of a given system. About a decade later an English Mathematician Edward Routh and, independently after two more decades a Swiss mathematician Adolf Hurwitz attempted the problem and provided both sufficient and necessary conditions, which we popularly call today as the Routh-Hurwitz criterion. This paper examines the problem of testing the stability of a given characteristic polynomial from a purely computational perspective. More precisely, we present a computationally faster algorithm which runs in O(n), saving the running time by an order when compared to the conventional R-H criterion.

Keywords: stability; Routh-Hurwitz criterion; Hurwitz determinant; algebraic transformations; time complexity; characteristic polynomials.

DOI: 10.1504/IJSCC.2013.055977

International Journal of Systems, Control and Communications, 2013 Vol.5 No.2, pp.166 - 176

Received: 29 Dec 2012
Accepted: 04 Apr 2013
Published online: 12 Jul 2014 *

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