The index and split forms of linear differential-algebraic equations
Differential-algebraic equations (DAEs) composed by linear systems of ordinary differential equations (ODE) with rectangular matrices of coefficients are considered, including the case when the matrix before the derivative of the desired vector function has not full rank for all argument values from the domain. Criteria for the existence of nonsingular transformations splitting the system into subsystems are obtained, whose solution can be written down analytically using generalized inverse matrices. The resulting solution formula is called a generalized split form of a DAE and can be viewed as a certain analogue of the Weierstrass-Kronecker canonical form. In particular, it is shown that arbitrary DAEs with rectangular coefficient matrices are locally reducible to a generalized split form.
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