Solvability Conditions, Consistency and Weak Consistency for Linear Differential-Algebraic Equations and Time-Invariant Singular Systems: The General Case.

摘要

The paper presents several solvability concepts for linear differential-algebraic equations (DAEs) with constant coefficients on the positive time-axis as well as for the associated singular systems, and investigates under which conditions these concepts are met. Next, it derives necessary and sufficient conditions for global consistency of initial conditions for the DAE as well as for the system, and generalizes these conditions with respect to the concept of weak consistency. This distributional approach enables one to generalize results in an earlier paper, where singular systems are assumed to have a regular pencil in the sense of Gantmacher. In particular, it establishes that global weak consistency in the system sense is equivalent to impulse controllability.