Matrix generic rank

In order to analyze estimability utilizing such ideas, we first include some notions related to structure. Then we define the concepts of structural observability and the generic rank of a matrix. 

The generic rank of a structured matrix B is defined to be the maximal rank that B achieves as a function of its free parameters. 

The maximal rank of an (m x g) matrix having no specified structure is equal to min (m, g). The inclusion of the structure into the problem makes it possible for matrices to have less than full rank, independent of the values of the free parameters, as was shown by Schields and Pearson (1976). Therefore, a structured matrix B has full generic rank if, and only if, there exists an admissible matrix B with full rank. 

By a natural extension of the concepts developed in the previous chapter (structural estimability), if the generic rank of the composite matrix (Aj A2) is not less than n (n number of unmeasured variables), then the system does not include structural singularities. Furthermore, if all the unmeasured nodes are determinable, then there are no isolated variables, which cannot be computed from the balance equations. 

The generic rank of the composite matrix (Ai A2) is not less than n... 

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