Galerkin projections for some wave and plate boundary control problems

References

• Cooke , K.L. and Grossman , Z. 1982 . Discrete delays, distributed delays and stability switches, . Math. Anal. and Appl., , 86 : 592 – 627 .
   Web of Science ®Google Scholar
• Datko , R. , Lagnese , J. and Polis , M.P. 1986 . An example of the efect of time delays in boundary feedback stabilization of wave equations, . SIAM J. Control Optim., , 24 : 152 – 156 .
   Web of Science ®Google Scholar
• Datko , R. 1988 . Not all feedback stabilized hyperbolic systems are robust with respect to small delays in their feedbacks, . SIAM J. Control Optim., , 26 : 697 – 713 .
   Web of Science ®Google Scholar
• Datko , R. 1991 . Two questions concerning the boundary control of certain elastic systems . Jour. Diff. Eqs., 92 , 92 : 27 – 44 .
   Google Scholar
• Datko R. Two examplesof ill-posedness with respect to small time delays in stabilized elastic systems submitted for publication.
   Google Scholar
• Datko R. You Y.C. ome second-order vibrating systems cannot tolerate small time delays in their damping, to appear Jour. Optim. Theory amd Appl.
   Google Scholar
• Kalman , R.E. 1960 . Contributions to the the0 y of optimal control, . Bol. Soc. Mat. Mexicano, , : 102 – 119 .
   Google Scholar
• Kamen , E.W. 1982 . Linear systems with commensurate time delays: Stability and stabilization independent of delay, . IEEE Trans. Automat. Control, , 27 : 367 – 375 .
   Web of Science ®Google Scholar
• Triggiani , R. 1990 . “ Further results on exact controllability of Euler-Bernoulli equations with controls in the Dirchlet and Neumann conditions, ” . Vol. 147 , Springer-verlag, .
   Google Scholar
• Lions , J.L. 1968 . Controle optimal de Systèmes gouverné par équation aux dérivées partielles, , Paris : Dunod .
   Google Scholar
• Lions , J.L. and Magenes , E. 1968 . Problemes aux limites non homegènes and application, , Paris : Dunod .
   Google Scholar
• Lions , J.L. 1988 . Exact controllability, stabilization and perturbations for distributed systems, . SIAM Review, , 30 : 1 – 68 .
   Web of Science ®Google Scholar
• Micheletti , A.M. 1976 . “ Perturbatione dello spettro di un opperatore ellitico ditipo variazaionale ” . In in realzione ad una variazione del campo , Vol. XXV , Fasc. II : Richerche de mathernatica .
   Google Scholar
• Ourada , N. and Triggiani , R. 1991 . Uniform stabilization of the Euler-Bernoulli equation with boundary feedback operator only in the Neumann boundary condition, . Diff. and Integral Eqs., , 4 : 277 – 292 .
   Google Scholar
• Triggiani , R. “ Lack of exact controllability for wave and plate equations with finitely many boundary controls ” . In Diff. amd Integral Eqs. to appear,
   Google Scholar
• Uspensky , J.V. 1948 . Theory of Equations, New York : McGraw Hill Inc., .
   Google Scholar