Certain algebraic procedures for Stability analysis of linear systems With complex coefficients

Abstract

newlineThe objective of this research work is to formulate certain criteria to newlineanalyse stability of complex polynomials that arise in engineering systems In newlinegeneral a characteristic equation with real coefficients is employed for newlinestability analysis of a linear time invariant systems But certain class of newlineapplications like relative and aperiodic stability analysis in linear timeinvariant newlinecontinuous systems involves complex coefficient polynomials In the newlinecase of certain time delay systems as well as two dimensional systems the newlineanalysis is done with complex polynomials The applications of complex newlinepolynomials also arise in case of nonlinear systems and systems with newlineinduction machines newlineIn this thesis two different algebraic schemes are formulated to handle newlinethe complex polynomials for analysing system stability In both the schemes newlinetermed as Sign Pair Criteria SPC I and SPC II Routh like table is developed newlineand the elements in the first column are utilized for stability analysis In the newlineproposed first scheme the first two rows are formed directly using complex newlinecoefficients while in the second scheme the real and imaginary parts of the newlinegiven complex polynomial are separated and the coefficients of real and newlineimaginary parts are entered in the first two rows of Routh like table newlineThese two sign pair criteria are applied to linear time invariant newlinecontinuous systems represented by complex polynomials having onedimension newlineas well as two dimensions for inferring stable and unstable newlinesituation including certain design problem newline newline