Recursive identification method for Hammerstein-Wiener system

In this paper a new identification method is put forward to deal with a kind of Hammerstein-Wiener systems, in which the first nonlinear is piecewise linear character. The study of this kind of Hammerstein-Wiener system is foundation of studying more general H-W system. The proposed model and method is brand new. By introducing a suitable instrumental variable, an algorithm is presented to recursively estimate the linear subsystems and the first nonlinearity with piecewise linear characteristic using stochastic approximation algorithm, and the second nonlinear function using kernel estimation method. Under some mild conditions, all the proposed estimates are proved to be strongly consistent.