文章基本信息

标题：Illustrative Study on Linear Differential Equations and Matrix Polynomials
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作者：JASPREET SINGH
期刊名称：International Journal of Electronics and Computer Science Engineering
电子版ISSN：2277-1956
出版年度：2013
卷号：2
期号：1
页码：32-38
出版社：Buldanshahr : IJECSE
摘要：The objective of this paper is to study the theoretical analysis of linear differential-algebraic equations (DAEs) of higher order as well as the regularity and singularity of matrix polynomials. Some invariants and condensed forms under appropriate equivalent transformations are established for systems of linear higher-order DAEs with constant and variable coefficients. Inductively, based on condensed forms, the properties of corresponding system of DAEs are studied and by differentiation-and-elimination steps reduce the system to a simpler but equivalent system. It includes the consistency of initial conditions and unique solvability of the original DAE system. It is shown that the following equivalence holds for a DAE system with strangeness-indexm and square and constant coefficients: for any consistent initial condition and any right-hand side f(t)Î Cμ([t0, t1],Cn) the associated initial value problem has a unique solution if and only if the matrix polynomial associated with the system is regular. Moreover, some necessary and sufficient conditions for column-and-row regularity and singularity of rectangular matrix polynomials are derived. A geometrical characterization of singular matrix pencils is also described. Furthermore, an algorithm is presented which using rank information about the coefficient matrices and via computing determinants decides whether a given matrix polynomial is regular.
关键词：Linear DAEs of higher order; strangeness-index; condensed form; matrix polynomial; regularity/ singularity of;matrix polynomial; matrix pencil; nearness to singularity.