A new approach to the index of differential-algebraic equations based on the index of matrix pencil
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Abstract
Differential-algebraic equations (DAEs) play an important role in many applied models, yet their analysis is complicated by algebraic constraints. A central difficulty is the definition of the index. We propose a new index definition for DAEs based on the classical index of a matrix pencil. This approach ensures projection independence and provides explicit solution formulas for DAEs of index at most two, while also clarifying the relation to März’s index.
Keywords
Differential-algebraic equations (DAEs), index 2, index of a matrix pencil
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References
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