Constant Coefficients Linear Higher Order Differential-Algebraic Equations

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Abstract

This paper contributes to the theoretical analysis of linear Differential Algebraic Equations of higher order as well as of the regularity and singularity of ma¬trix polynomials. Some invariants and condensed forms under appropriate equivalent transformations are given for systems of linear higher-order Differential-Algebraic Equations’ with constant and variable coefficients. Inductively, based on condensed forms the original Differential-Algebraic Equations system can be transformed by differentiation-and-elimination steps into an equivalent strangeness-free system, from which the solution behaviour (including consistency of initial conditions and unique solvability) of the original Differential-Algebraic Equations system and related initial value problem can be directly read off.