By E. Walter
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Additional info for Identifiability of Parametric Models
The number of do mains defined in the parametric space, which is 7 dimensional, is therefore also equal to 3. The strong separator defined in (48) thus esta blishes three connected domains, and the identi fication problem has precisely 3 distinct solutions. i v' We know that the determinant of matrix K C K is zero in subsets wich dimension (d-1) where d is the parameter space dimension. These subsets are called separators and divide parametric space in to several parts. If the equations are linear the separators define two distinct parts, but for non-linear equations the number of regions thus formes may exceed two.
Both measurement gains have been assumed known. 4) we see a 4 5 » °25 35 this gives 6 equations in 6 unknowns, including IV P 8' P '12· This is represented in the last row of Table 1, where the 2nd column gives the subscripts of those elements of P involved and the last column equals, (the number of unknowns)-(the number of equations) bolumns TABLE 1 indices of V ~ i No. of unknownsNo. of equations 7 3 2 -1 1,3,4,5,7,8,9,11,12 1,2,5,6,9,10 1,2,5,6,9,10 3,7,11 4,8,12 1 2 3 4 5 o This table suggests a method (B) analysis might prove useful on columns 4 and 5.
R together with the unknown 1 Also, entries of P in columns k, k φ i s if this does not include k = j , which can only occur if a.. e. if compartment j is a trap, the unknowns in column j of P - 1 must be added. , ψ 0, the total number of unknowns 3D can simply be found by adding to the number of nonzero entries in the jth column of A, the number of unknown elements in P lying in columns with the same index as the rows_in which the forementioned nonzero entries of A lie. k Ï j £/ A =_1, 2,. , s together with the unknown entries of P in rows k, k φ j .