Robust Stabilization of the Navier–Stokes Equation via the H-Control Theory

  • Viorel Barbu
Part of the Communications and Control Engineering book series (CCE)


Since most of the fluid dynamic systems are subject to uncertainties and external disturbances, a major problem is the design of feedback controllers which achieve asymptotic stability not only for a nominal system (which is only partially known) but also for an entire set of systems covering a neighborhood of the given system. Such a control is called robust and the H -control theory provides an efficient and popular approach to this question. We discuss in some details the H -control problem for the stabilization problems studied in Chap. 3. We begin with a general presentation and some basic results on the H -control problem for linear infinite-dimensional systems.


Control Problem Hamiltonian System Invariant Manifold Feedback Controller Mild Solution 
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  1. 8.
    Barbu V (1992) H -boundary control with state feedback; the hyperbolic case. Int. Ser. Numer. Math. 107:141–148 MathSciNetGoogle Scholar
  2. 9.
    Barbu V (1994) Mathematical Methods in Optimization of Differential Systems. Kluwer, Dordrecht MATHCrossRefGoogle Scholar
  3. 10.
    Barbu V (1995) The H -problem for infinite dimensional semilinear systems. SIAM J. Control Optim. 33:1017–1027 MathSciNetMATHCrossRefGoogle Scholar
  4. 25.
    Barbu V, Sritharan S (1998) H -control theory of fluid dynamics. Proc. R. Soc. Lond. A 454:3009–3033 MathSciNetMATHCrossRefGoogle Scholar
  5. 32.
    Bensoussan A, Da Prato G, Delfour M (1992) Representation and Control of Infinite Dimensional Systems. Birkhäuser, Boston, Basel, Berlin MATHGoogle Scholar
  6. 33.
    Bewley TR (2001) Flow control: new challenge for a new Renaissance. Prog. Aerosp. Sci. 37:21–50 CrossRefGoogle Scholar
  7. 34.
    Bewley T, Temam R, Ziane M (2000) A general framework for robust control in fluid mechanics. Physica D 138:360–392 MathSciNetMATHCrossRefGoogle Scholar
  8. 47.
    Doyle J, Glover K, Khargonekar P, Francis B (1989) State space solutions to standard H 2 and H −∞-control problems. IEEE Trans. Autom. Control AC 34:831–847 MathSciNetMATHCrossRefGoogle Scholar
  9. 77.
    Van Der Schaft AJ (1991) A state space approach to nonlinear H control. Syst. Control Lett. 16:1–8 MATHCrossRefGoogle Scholar
  10. 78.
    Van Der Schaft AJ (1993) L 2 gain analysis of nonlinear systems and nonlinear state feedback H control. IEEE Trans. Autom. Control 37:770–784 CrossRefGoogle Scholar
  11. 79.
    Van Keulen B (1993) H -control for Distributed Parameter Systems: A State-Space Approach. Birkhäuser, Boston, Basel, Berlin MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Fac. MathematicsAl. I. Cuza UniversityIaşiRomania

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