Synthesis via a Parameterized ARE Approach or a Parameterized LMI Approach

  • Sophie TarbouriechEmail author
  • Germain Garcia
  • João Manoel Gomes da SilvaJr.
  • Isabelle Queinnec


This chapter deals with the problem of control design taking into account control amplitude limitation and the performance level through a quadratic criterion. Two approaches are presented for solving the problem. The first one is developed using the properties of an adequate parameterized Riccati equation. The second one is an alternate way, derived in terms of parameterized LMIs. Even if the two approaches are intimately connected, each of them possesses a specific interest. The Riccati equation approach is elegant, in some sense analytical, and allows one to enter into the structural properties of the problem. The LMI approach is easier to derive, numerically powerful and adapted for easily taking into account other constraints like for example constrained control structures or maximization of volume of the attraction domain or its approximations. Some extensions are also proposed. In particular, the problems of multi-objective control (quadratic criterion and pole placement), disturbance rejection and control of time-delay systems are addressed.


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Sophie Tarbouriech
    • 1
    Email author
  • Germain Garcia
    • 2
  • João Manoel Gomes da SilvaJr.
    • 3
  • Isabelle Queinnec
    • 1
  1. 1.Laboratoire Analyse et Architecture des Systèmes (LAAS)CNRSToulouse CX 4France
  2. 2.Laboratoire Analyse et Architecture des Systèmes (LAAS)CNRSToulouse CX 4France
  3. 3.Departamento de Engenharia ElétricaUniversidade Federal do Rio Grande do SulPorto AlegreBrazil

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