Abstract
Descriptor variable systems consist of a mixture of static and dynamic equations. This paper investigates the structural characteristics of linear time-invariant descriptor systems and develops an efficient technique for converting a descriptor system to recursive form, if such a conversion is possible. The paper exploits the connection between descriptor systems and the classical theory of matrix pencils. This yields a canonical form for descriptor systems. The main contribution of the paper is the shuffle algorithm. This algorithm serves both as a test for the solvability of a descriptor system, and as a procedure for converting a system to recursive form, without a change of variable.
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