Existence of stationary points for pseudo-linear regression identification algorithms

The authors prove existence of a stable transfer function satisfying the nonlinear equations characterizing an asymptotic stationary point, in undermodeled cases, for a class of pseudo-linear regression algorithms, including Landau’s algorithm, the Feintuch algorithm, and (S)HARF. The proof applies to all degrees of undermodeling and assumes only that the input power spectral density function is bounded and nonzero for all frequencies and that the compensation filter is strictly minimum phase. Some connections to previous stability analyses for reduced-order identification in this algorithm class are brought out.