Existence of stationary points for pseudo-linear regression identificationalgorithms

The authors prove existence of a stable transfer function satisfying the no nlinear equations characterizing an asymptotic stationary point, in undermo deled 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 spect ral density function is bounded and nonzero for all frequencies and that th e compensation filter is strictly minimum phase. Some connections to previo us stability analyses for reduced-order identification in this algorithm cl ass are brought out.