The analysis of exact controllability of neutral-type systems by the moment problem approach

SIAM Journal on Control and Optimization

Volumn 46, Issue 6, 2007, Pages 2148-2181

  Rabah, Rabah ^a   Sklyar, Grigory M ^b  

^a ECOLE DES MINES DE NANTES   (France)

^b UNIVERSITY OF SZCZECIN   (Poland)

Author keywords

Distributed delays; Exact controllability; Moment problem; Neutral type systems; Riesz basis

Indexed keywords

BANACH SPACES; CODES (SYMBOLS); CONTROLLABILITY; HILBERT SPACES;

DISTRIBUTED DELAYS; EXACT CONTROLLABILITY; MOMENT PROBLEM; NEUTRAL-TYPE SYSTEMS; RIESZ BASIS;

CONTROL THEORY;

EID: 44149126184     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060650246     Document Type: Article

References (17)

1. S. A. AVDONIN AND S. A. IVANOV, Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems, Cambridge University Press, Cambridge, UK, 1995.
2. (1) of linear hereditary systems, SIAM J. Control, 13 (1975), pp. 611-649.
3. 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), pp. 98-116.
4. I. C. GOHBERG AND M. G. KREIN, Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monogr. 18, AMS, Providence, RI, 1969.
5. K. ITO AND T. J. TARN, A linear quadratic optimal control for neutral systems, Nonlinear Anal., 9 (1985), pp. 699-727.
6. M. Q. JACOBS AND C. E. LANGENHOP, Criteria for function space controllability of linear neutral systems, SIAM J. Control Optim., 14 (1976), pp. 1009-1048.
7. L. A. LIUSTERNIK AND V. J. SOBOLEV, Elements of Functional Analysis, Russian Monographs and Texts on Advanced Mathematics and Physics, 5, Hindustan Publishing, Delhi, Gordon and Breach Publishers, New York, 1961.
8. A. MANITIUS AND R. TRIGGIANI, Function space controllability of linear retarded systems: A derivation from abstract operator conditions, SIAM J. Control Optim., 16 (1978), pp. 599-645.
9. D. A. O'CONNOR AND T. J. TARN, On the function space controllability of linear neutral systems, SIAM J. Control Optim., 21 (1983), pp. 306-329.
10. 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), pp. 19-24.
11. R. RABAH, G. M. SKLYAR, AND A. V. REZOUNENKO, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations, 214 (2005), pp. 391-428.
12. H. RIVERA RODAS AND C. E. LANGENHOP, A sufficient condition for function space controllability of a linear neutral system, SIAM J. Control Optim., 16 (1978), pp. 429-435.
13. W. RUDIN, Functional Analysis, 2nd ed., McGraw-Hill, New York, 1991.
14. D. ULLRICH, Divided differences and systems of nonharmonic Fourier series, Proc. Amer. Math. Soc., 80 (1980), pp. 47-57.
15. W. M. WONHAM, Linear Multivariable Control: A Geometric Approach, Springer, New York, 1985.
16. Y. YAMAMOTO, Reachability of a class of infinite-dimensional systems: An external approach with applications to general neutral systems, SIAM J. Control Optim., 27 (1989), pp. 217-234.
17. R. Y. YOUNG, An Introduction to Nonharmonic Analysis, Academic Press, New York, 1980.