Identifiability of nonlinear Hammerstein plants (Q1077370)

A Hammerstein plant means that in this plant the nonlinear part without lag is in front of the linear part. This paper considers a one- dimensional discrete stationary open-loop Hammerstein plant described by the equation \[ u_ t=W(z^{-1};\alpha)z^{-\tau}f(x_ t;\theta)+H(z^{-1},h)\xi_ t, \] where \[ W(z^{- 1};\alpha)=\sum^{n_ b}_{i=0}b_ iz^{-i}/(1+\sum^{n_ b}_{i=1}a_ iz^{-i}), \] \[ H(z^{-1};h)=(1+\sum^{n_ b}_{i=1}p_ iz^{-i})/(1+\sum^{n_ r}_{i=1}r_ iz^{-i})\quad and\quad f(x_ t;\theta)=\sum^{n_{\theta}}_{i=1}\theta_ i\phi_ i(x_ t), \] and obtains the identifiability conditions under random disturbances with unknown rational-fraction spectral densities, which are in the form of requirements towards the input signal and the information needed with regard to the orders of the plant polynomials.