Variable classification using matrix projection

An elegant classification strategy using projection matrices was proposed by Crowe et al. (1983) for linear systems and extended later (Crowe, 1986, 1989) to bilinear ones. Crowe suggested a useful method for decoupling the measured variables from the constraint equations, using a projection matrix to eliminate the unmeasured process variables. 

For linear plant models Crowe et al. (1983) used a projection matrix to obtain a reduced system of equations that allows the classification of measured variables. They identified the unmeasured variables by column reduction of the submatrix corresponding to these variables. 

This chapter is devoted to the analysis of variable classification and the decomposition of the data reconciliation problem for linear and bilinear plant models, using the so-called matrix projection approach. The use of orthogonal factorizations, more precisely the Q-R factorization, to solve the aforementioned problems is discussed and its range of application is determined. Several illustrative examples are included to show the applicability of such techniques in practical applications. 

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