In the context of model inversion, a structural invariant of the transfer matrix, the essential order, is used as a model specification criterion to determine the highest time-differentiation order reached by an output in the inverse model. Originally defined for linear timeinvariant (LTI) regular systems, we propose an algebraic extension to the class of LTI descriptor systems with regular matrix pencil and show that, from a descriptor system inversion viewpoint, this invariant characterizes the highest time-differentiation of the output like in the regular case. A bond graph determination procedure on the direct model is given using (bi)causal path inspection and the notion of families of different causal paths.
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