International Journal of Dynamics and Control

, Volume 7, Issue 4, pp 1453–1461 | Cite as

A new Hammerstein model control strategy: feedback stabilization and stability analysis

  • Zeineb RayoufEmail author
  • Chekib Ghorbel
  • Naceur Benhadj Braiek


This paper treats the identification, the control and the stability analysis of the discrete Hammerstein structure which is composed by a static nonlinearity gain associated with a linear dynamic subsystem. Its parameters are obtained from the subspace identification using the multivariable output error state space algorithm. The stabilization of this class of systems is generally leaded by a nonlinear control law, including an exact inverse of the static nonlinearity. Then, it is possible to use a linear state feedback controller to stabilize the Hammerstein system in closed-loop and to track the reference input. Thus, the performances of this method become limited when the considered static nonlinearity is approximately invertible. In this context, an approximate inverse of this component is investigated. Furthermore, based on the Lyapunov method, the stability conditions are obtained by solving a set of linear matrix inequalities constraints. The case of a coupled two-tank system is considered in order to illustrate the validity of the proposed approach.


Hammerstein structure Subspace identification MOESP algorithm Lyapunov method LMI Stability analysis Sector nonlinearity 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zeineb Rayouf
    • 1
    Email author
  • Chekib Ghorbel
    • 1
  • Naceur Benhadj Braiek
    • 1
  1. 1.Advanced System LaboratoryPolytechnic School of TunisiaEl MarsaTunisia

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