Free Access
Issue
ESAIM: COCV
Volume 18, Number 3, July-September 2012
Page(s) 656 - 692
DOI https://doi.org/10.1051/cocv/2011166
Published online 19 September 2011
  1. W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups. Trans. Am. Math. Soc. 306 (1988) 837–852. [Google Scholar]
  2. A. Bátkai, K.-J. Engel, J. Prüss and R. Schnaubelt, Polynomial stability of operator semigroups. Math. Nachr. 279 (2006) 1425–1440. [CrossRef] [MathSciNet] [Google Scholar]
  3. R. Bellman and K.L. Cooke, Differential-difference equations. Academic Press, New York (1963). [Google Scholar]
  4. C. Bonnet, A.R. Fioravanti and J.R. Partington, On the stability of neutral linear systems with multiple commensurated delays, in IFAC Workshop on Control of Distributed Parameter Systems. Toulouse (2009) 195–196. IFAC/LAAS-CNRS. [Google Scholar]
  5. A. Borichev and Y. Tomilov, Optimal polynomial decay of functions and operator semigroups. Math. Ann. 347 (2010) 455–478. [Google Scholar]
  6. W.E. Brumley, On the asymptotic behavior of solutions of differential-difference equations of neutral type. J. Diff. Equ. 7 (1970) 175–188. [CrossRef] [Google Scholar]
  7. J.A. Burns, T.L. Herdman and H.W. Stech, Linear functional-differential equations as semigroups on product spaces. SIAM J. Math. Anal. 14 (1983) 98–116. [CrossRef] [MathSciNet] [Google Scholar]
  8. R.F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory, Texts in Applied Mathematics 21. Springer-Verlag, New York (1995). [Google Scholar]
  9. X. Dusser and R. Rabah, On exponential stabilizability of linear neutral type systems. Math. Probl. Eng. 7 (2001) 67–86. [Google Scholar]
  10. J.K. Hale and S.M.V. Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences 99. Springer-Verlag, New York (1993). [Google Scholar]
  11. J.K. Hale and S.M.V. Lunel, Strong stabilization of neutral functional differential equations. IMA J. Math. Control Inf. 19 (2002) 5–23. Special issue on analysis and design of delay and propagation systems. [CrossRef] [Google Scholar]
  12. D. Henry, Linear autonomous neutral functional differential equations. J. Diff. Equ. 15 (1974) 106–128. [CrossRef] [Google Scholar]
  13. C.A. Jacobson and C.N. Nett, Linear state-space systems in infinite-dimensional space : the role and characterization of joint stabilizability/detectability. IEEE Trans. Automat. Control 33 (1988) 541–549. [CrossRef] [MathSciNet] [Google Scholar]
  14. T. Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer-Verlag New York, Inc., New York (1966). [Google Scholar]
  15. V.B. Kolmanovskii and V.R. Nosov, Stability of functional-differential equations, Mathematics in Science and Engineering 180. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London (1986). [Google Scholar]
  16. L.A. Liusternik and V.J. Sobolev, Elements of functional analysis, Russian Monographs and Texts on Advanced Mathematics and Physics 5. Hindustan Publishing Corp., Delhi (1961). [Google Scholar]
  17. Z.-H. Luo, B.-Z. Guo and O. Morgul, Stability and stabilization of infinite dimensional systems with applications. Communications and Control Engineering Series, Springer-Verlag London Ltd., London (1999). [Google Scholar]
  18. Yu.I. Lyubich and V.Q. Phóng, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 37–42. [MathSciNet] [Google Scholar]
  19. S.A. Nefedov and F.A. Sholokhovich, A criterion for stabilizability of dynamic systems with finite-dimensional input. Differentsial’ nye Uravneniya 22 (1986) 223–228, 364. [Google Scholar]
  20. D.A. O’Connor and T.J. Tarn, On stabilization by state feedback for neutral differential-difference equations. IEEE Trans. Automat. Control 28 (1983) 615–618. [CrossRef] [MathSciNet] [Google Scholar]
  21. L. Pandolfi, Stabilization of neutral functional differential equations. J. Optim. Theory Appl. 20 (1976) 191–204. [Google Scholar]
  22. J.R. Partington and C. Bonnet, H and BIBO stabilization of delay systems of neutral type. Syst. Control Lett. 52 (2004) 283–288. [Google Scholar]
  23. L.S. Pontryagin, On the zeros of some elementary transcendental functions. Amer. Math. Soc. Transl. 1 (1955) 95–110. [MathSciNet] [Google Scholar]
  24. R. Rabah and G.M. Sklyar, Strong stabilizability for a class of linear time delay systems of neutral type. Mat. Fiz. Anal. Geom. 11 (2004) 314–330. [MathSciNet] [Google Scholar]
  25. R. Rabah and G.M. Sklyar, On a class of strongly stabilizable systems of neutral type. Appl. Math. Lett. 18 (2005) 463–469. [Google Scholar]
  26. R. Rabah and G.M. Sklyar, The analysis of exact controllability of neutral-type systems by the moment problem approach. SIAM J. Control Optim. 46 (2007) 2148–2181. [Google Scholar]
  27. R. Rabah, G.M. Sklyar and A.V. Rezounenko, Generalized Riesz basis property in the analysis of neutral type systems. C. R. Math. Acad. Sci. Paris 337 (2003) 19–24. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Rabah, G.M. Sklyar and A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space. J. Diff. Equ. 214 (2005) 391–428. [CrossRef] [Google Scholar]
  29. R. Rabah, G.M. Sklyar and A.V. Rezounenko, On strong regular stabilizability for linear neutral type systems. J. Diff. Equ. 245 (2008) 569–593. [CrossRef] [Google Scholar]
  30. G.M. Sklyar, Lack of maximal asymptotics for some linear equations in a Banach space. Dokl. Math. 81 (2010) 265–267. Extended version to appear in Taiwanese Journal of Mathematics (2011). [CrossRef] [MathSciNet] [Google Scholar]
  31. G.M. Sklyar and A.V. Rezounenko, Stability of a strongly stabilizing control for systems with a skew-adjoint operator in Hilbert space. J. Math. Anal. Appl. 254 (2001) 1–11. [Google Scholar]
  32. G.M. Sklyar and A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 807–812. [CrossRef] [MathSciNet] [Google Scholar]
  33. G.M. Sklyar and V.Ya. Shirman, On asymptotic stability of linear differential equation in Banach space. Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 37 (1982) 127–132. [Google Scholar]
  34. R. Triggiani, On the stabilizability problem in Banach space. J. Math. Anal. Appl. 52 (1975) 383–403. [Google Scholar]
  35. J. van Neerven, The asymptotic behaviour of semigroups of linear operators, Operator Theory : Advances and Applications 88. Birkhäuser Verlag, Basel (1996). [Google Scholar]
  36. S.M. Verduyn Lunel and D.V. Yakubovich, A functional model approach to linear neutral functional-differential equations. Integr. Equ. Oper. Theory 27 (1997) 347–378. [CrossRef] [Google Scholar]
  37. V.V. Vlasov, Spectral problems that arise in the theory of differential equations with delay. Sovrem. Mat. Fundam. Napravl. 1 (2003) 69–83 (electronic). [Google Scholar]
  38. W.M. Wonham, Linear multivariable control, Applications of Mathematics 10. 3th edition, Springer-Verlag, New York (1985). [Google Scholar]

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