Free Access
Volume 21, Number 2, April-June 2015
Page(s) 535 - 560
Published online 09 March 2015
  1. M. Badra, Lyapunov function and local feedback boundary stabilization of the Navier–Stokes equations. SIAM J. Control Optim. 48 (2009) 1797–1830. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Badra, Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier–Stokes and Boussinesq equations with Neumann or Dirichlet control. Discrete Contin. Dyn. Syst. 32 (2012) 1169–1208. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Badra and T. Takahashi, Stabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers: application to the Navier–Stokes system. SIAM J. Control Optim. 49 (2011) 420–463. [CrossRef] [MathSciNet] [Google Scholar]
  4. H.T. Banks, R.C. Smith and Y. Wang, Smart Material Structures, modeling, estimation and control. Masson/John Wiley, Paris/Chichester (1996). [Google Scholar]
  5. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Vol. 1. Birkhäuser, Boston (1992). [Google Scholar]
  6. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Vol. 2. Birkhäuser, Boston (1992). [Google Scholar]
  7. J. Burns and H. Marrekchi, Optimal fixed-finite-dimensional compensator for Burgers’ equation with unbounded input/output operators, Computation and Control III. Progress System Control Theory. Vol. 15. Birkhauser, Boston, MA (1993) 83–104. [Google Scholar]
  8. J. Burns, A. Balogh, D.S. Gilliam and V.I. Shubov, Numerical Stationary Solutions for a Viscous Burgers’ Equation. J. Math. Syst. Estim. Control 8 (1998) 1–16. [Google Scholar]
  9. C.M. Chen and V. Thomée, The lumped mass finite element method for a parabolic problem. J. Austral. Math. Soc. Ser. B 26 (1985) 329–354. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.-M. Coron, Control and nonlinearity. American Mathematical Society. Providence, RI (2007). [Google Scholar]
  11. R. Curtain, Finite dimensional compensators for parabolic distributed systems with unbounded control and observation. SIAM J. Control Optim. 22 (1984) 255–276. [CrossRef] [MathSciNet] [Google Scholar]
  12. R. Curtain, A comparison of finite-dimensional controller designs for distributed parameter systems, Control Theory Adv. Technol. 9 (1993) 609–628. [Google Scholar]
  13. R. Curtain and D. Salamon, Finite dimensional compensators for infinite dimensional systems with unbounded input operators. SIAM J. Control Optim. 24 (1986) 797–816. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Curtain and H.J. Zwart, An introduction to infinite dimensional linear systems theory. Springer-Verlag, New York (1995). [Google Scholar]
  15. H.C. Elman, D.J. Silvester and A.J. Wathen, Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics. Oxford University Press, New York (2005). [Google Scholar]
  16. A.V. Fursikov, Optimal control of distributed systems. Theory and Applications. AMS Providence, Rhode Island (2000). [Google Scholar]
  17. P. Grisvard, Caractérisation de quekques espaces d’interpolation. Arch. Rat. Mech. An. 25 (1967) 40–63. [Google Scholar]
  18. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman Monogr. Studies in Mathematics. Vol. 24. Advanced Publishing Program, Boston, MA (1985). [Google Scholar]
  19. P. Grisvard, Singularities in boundary value problems. Recherches en Mathématiques Appliquées [Research in Applied Mathematics]. Vol. 22. Masson, Paris; Springer-Verlag, Berlin (1992). [Google Scholar]
  20. G. Ji and I. Lasiecka, Partially observed analytic systems with fully unbounded actuators and sensors-FEM algorithms. Comput. Optim. Appl. 11 (1998) 111–136. [CrossRef] [Google Scholar]
  21. S. Jund and S. Salmon, Arbitrary high-order finite element schemes and high-order mass lumping. Int. J. Appl. Math. Comput. Sci. 17 (2007) 375–393. [CrossRef] [MathSciNet] [Google Scholar]
  22. T. Kato, Perturbation theory for linear operators, Reprint of the 1980 Edition. Springer-Verlag (1995). [Google Scholar]
  23. S. Kesavan and J.P. Raymond, On a degenerate Riccati equation. Control Cybern. 38 (2009) 1393–1410. [Google Scholar]
  24. I. Lasiecka, Galerkin approximations of infinite dimensional compensators for flexible structures with unbounded control action. Acta Appl. Math. 28 (1992) 101–133. [CrossRef] [Google Scholar]
  25. I. Lasiecka, Finite element approximations of compensator design for analytic generators with fully unbound controls/observations. SIAM J. Control Optim. 33 (1995) 67–88. [CrossRef] [MathSciNet] [Google Scholar]
  26. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximations Theories. Vol. I. Cambridge University Press, Cambridge (2000). [Google Scholar]
  27. A.J. Laub, A Schur method for solving algebraic Riccati equations. IEEE Trans. Automat. Control 24 (1979) 913–925. [CrossRef] [MathSciNet] [Google Scholar]
  28. J.-L. Lions, Contrôle optimal des équations aux dérivées partielles. Dunod, Paris (1968). [Google Scholar]
  29. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. 2. Springer, Berlin-Heidelberg-New York (1972). [Google Scholar]
  30. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New-York (1983). [Google Scholar]
  31. J.P. Raymond, Boundary feedback stabilization of the two dimensional Navier–Stokes equations. SIAM J. Control Optim. 45 (2006) 790–828. [CrossRef] [MathSciNet] [Google Scholar]
  32. J.P. Raymond, Feedback boundary stabilization of the three dimensional incompressible Navier–Stokes equations. J. Math. Pures Appl. 87 (2007) 627–669. [CrossRef] [MathSciNet] [Google Scholar]
  33. J.P. Raymond, Stabilizability of infinite dimensional systems by finite dimensional controls, submitted. [Google Scholar]
  34. J.-P. Raymond and L. Thevenet, Boundary feedback stabilization of the two dimensional Navier–Stokes equations with finite dimensional controllers. Discrete Contin. Dyn. Syst. 27 (2010) 1159–1187. [Google Scholar]
  35. L.F. Shampine, I. Gladwell and S. Thompson, Solving ODEs with MATLAB. Cambridge University Press, Cambridge (2003). [Google Scholar]
  36. J.M. Schumacher, A direct approach to compensator design for distributed parameter systems. SIAM J. Control and Optim. 21 (1983) 823–836. [Google Scholar]
  37. L. Thevenet, Lois de feedback pour le contrôle d’écoulements. Ph.D. Thesis, Université de Toulouse (2009). [Google Scholar]
  38. L. Thevenet, J.-M. Buchot and J.-P. Raymond, Nonlinear feedback stabilization of a two-dimensional Burgers equation. ESAIM: COCV 16 (2010) 929–955. [CrossRef] [EDP Sciences] [Google Scholar]
  39. M. Tucsnak and G. Weiss, Observation and control for operator semigroups. Birkhuser Verlag, Basel (2009). [Google Scholar]

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