Robust stabilization and tracking control schemes for disturbed multi-input multi-output Hammerstein model in presence of approximate polynomial nonlinearities

Abstract

This article presents robust stabilization and tracking control problems for multi-input multi-output Hammerstein model with external disturbances. This model is characterized by static nonlinear elements followed by a linear dynamic block. Moreover, the unknown parameters of the identified mathematical model are estimated using the multivariable output error state space subspace algorithm. Unlike the general control strategy that used the nonlinearity inversion method, the nonlinearities are supposed not bijective. In this context, inverse nonlinear functions of polynomial structure are suggested in this article. Furthermore, the composition of the static nonlinear elements and their approximate inverses in series with the linear dynamic block are then decomposed into a set of linear parts using the Takagi–Sugeno fuzzy representation. Consequently, new sufficient stability conditions with decay rate and disturbance attenuation using the [Formula: see text] criterion and linear matrix inequality tools are discussed. Finally, simulation studies are provided to illustrate the merit of our purpose.