where the last two equations ensure that the residual is nonzero if there is a fault (ffc ^ 0). The equations for yk and rk and Eq. (8.95) lead to

The solution to Eqs. (8.96-8.97) is obtained by supplying the matrices R, S, J, Li, and L2. The solution details are given in [456]. However, Eq. (8.94) (nonzero and zero values for rfc) and Eq. (8.92) may not exactly be satisfied in many practical situations, and optimal approximations may be needed [163]. The procedure for finding optimal approximate solutions have been proposed [163].

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