Home   >   CSC-OpenAccess Library   >    Manuscript Information
Full Text Available

This is an Open Access publication published under CSC-OpenAccess Policy.
Publications from CSC-OpenAccess Library are being accessed from over 74 countries worldwide.
Certain Algebraic Procedures for the Aperiodic Stability Analysis and Counting the Number of Complex Roots of Linear Systems
K.Sreekala, S.N .Sivanandam
Pages - 212 - 219     |    Revised - 15-09-2012     |    Published - 25-10-2012
Volume - 3   Issue - 4    |    Publication Date - December 2012  Table of Contents
Complex Roots of a Polynomial, Linear Systems, Aperiodic Stability Analaysis, Modified Routh’s Table, Sign pair Criterion I and II
To evaluate the performance of a linear time-invariant system, various measures are available. In this paper employing Routh’s table, two geometrical criteria for the aperiodic stability analysis of linear time-invariant systems having real coefficients are formulated. The proposed algebraic stability criteria check whether the given linear system is aperiodically stable or not.The additional significance of the two criteria is , it can be used to count the number of complex roots of a system having real coefficients which is not possible by the use of original Routh’s Table. These procedures can also be used for the design of linear systems. In the proposed methods , the characteristic equation having real coefficients are first converted to complex coefficient equations using Romonov’s transformation. These complex coefficients are used in two different ways to form the Modified Routh’s tables for the two schemes named as Sign Pair Criterion I (SPC I) and Sign Pair Criterion II (SPC II). It is found that the proposed algorithms offer computational simplicity compared to other algebraic methods and is illustrated with suitable examples. The developed MATLAB program make the analysis most simple.
1 Google Scholar 
2 CiteSeerX 
3 refSeek 
4 Scribd 
5 SlideShare 
6 PdfSR 
1 E. Frank , “On the zeros of polynomials with complex coefficients”, Bull.Amer.Math.Soc,1946 pp. 144 – 158.
2 S.D.Agashe , “A new general Routh like Algorithm to determine the number of R H P Roots of a a real or complex polynomial”, I EEE Transactions on a automatic control ,1985,pp.406-409.
3 M.Benidt and B.Picinbon, “The extended Routh’s table in the complex case”, I EEE Transactions on Automatical Control,1991, pp. 253-256 .
4 Shyan S.Chen and Jason S.H.Tsai, “A new Tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis”. IEEE Transactions on Automatic Control, 1993, pp.1536-1541.
5 Adel M.K .Hashem, Network Synthesis of Complex Impedance and Complex Reactance Functions ,Ph.D Thesis, Concordia University, 1993.
6 S.N.Sivanandam and K.Sreekala, “An algebraic Approach for Stability Analysis of Linear Systems with Complex Coefficients”, International Journal of Computer Applications,2012,pp. 13-16.
7 A.T. Fuller, “Conditions for Aperiodicity in Linear Systems”, British Journal of Applied Physics, 1955,pp. 450-451.
8 E .I. Jury,Van , Inners and Stability of Dynamics Systems, New York, Wiley, 1974.
9 M.E .Van Valkenburg, Modern Network Synthesis, New York, Wiley, 1960, pp. 100-103.
10 Itzhack Bar – Itzhack and A nthony J. Calise,”Counting Complex Roots in Polynomials with Real Coefficients”,Proceedings of the IEEE, 1967, pp.2024-2026.
Associate Professor K.Sreekala
MET'S School of Engineering, Mala - India
Dr. S.N .Sivanandam
Karpagam College of Engineering - India