Boundary value problems for linear differential-algebraic equations: solvability via the Kronecker canonical form

RESUMO

The solvability of two-point boundary value problems for constant-coefficient differential-algebraic equations is investigated. Unlike previous studies, which often assume that the matrix pair associated with the equation is regular, we consider the general singular case. Using the Kronecker canonical form, we decompose the problem into simpler subsystems, enabling a systematic analysis of solvability. The method of parameterization reduces the boundary value problem to a system of algebraic equations. We derive criteria for the existence and uniqueness of solutions and provide a comprehensive framework for solving such boundary value problems. Several illustrative examples are presented and show the applicability of the results.