Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block

This note deals with identification of Hammerstein systems with discontinuous piecewise-linear memoryless block followed by a linear subsystem. Recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block. By taking a sequence of iid random variables with uniform distribution to serve as the system input, strong consistency is proved for all estimates given in the note. The theoretical results are verified by computer simulation.