Czasopismo
2012
|
Vol. 60, no 2
|
187--199
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
The paper studies the stabilization problem for a class of linear parabolic boundary control systems with a Riesz basis. The author earlier proposed two different feedback control schemes to cope with the difficulties arising from the feedback terms on the boundary; these schemes are based on different ideas, and look fairly different from each other. We show, however, that they are algebraically similar.
Rocznik
Tom
Strony
187--199
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Department of Applied Mathematics Graduate School of System Informatics Kobe University Nada, Kobe 657-8501, Japan, nambu@kobe-u.ac.jp
Bibliografia
- [1] S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton, 1965.
- [2] R. F. Curtain, Finite dimensional compensators for parabolic distributed systems with unbounded control and observation, SIAM J. Control Optim. 22 (1984), 255-276.
- [3] H. O. Fattorini, Boundary control systems, SIAM J. Control 6 (1966), 349-385.
- [4] P. Grabowski and F. M. Callier, Admissible observation operators. Duality of observation and control using factorizations, Dynam. Contin. Discrete Impulsive Systems 6 (1999), 87-119.
- [5] S. Itô, Diffusion Equations, Amer. Math. Soc., Providence, 1992.
- [6] T. Kato, A generalization of the Heinz inequality, Proc. Japan Acad. Ser. A Math. Sci. 37 (1961), 305-308.
- [7] N. Levinson, Gap and Density Theorems, Amer. Math. Soc. Colloq. Publ. 26, Amer. Math. Soc., New York, 1940.
- [8] J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer, New York, 1972.
- [9] T. Nambu, On stabilization of partial differential equations of parabolic type: Boundary observation and feedback, Funkcial. Ekvac. 28 (1985), 267-298.
- [10] |, An extension of stabilizing compensators for boundary control systems of parabolic type, J. Dynam. Differential Equations 1 (1989), 327-346.
- [11] |, An algebraic method of stabilization for a class of boundary control systems of parabolic type, ibid. 13 (2001), 59-85.
- [12] |, An L2(Ω)-based algebraic approach to boundary stabilization for linear parabolic systems, Quart. Appl. Math. 62 (2004), 711-748.
- [13] |, A new algebraic approach to stabilization for boundary control systems of parabolic type, J. Differential Equations 218 (2005), 136-158.
- [14] Y. Sakawa, Feedback stabilization of linear diffusion systems, SIAM J. Control Optim. 21 (1983), 667-676.
- [15] Y. Sakawa and T. Matsushita, Feedback stabilization of a class of distributed systems and construction of a state estimator, IEEE Trans. Automat. Control 20 (1975), 748-753.
- [16] M. Slemrod, Stabilization of boundary control systems, J. Differential Equations 22 (1976), 402-415.
- [17] A. E. Taylor, Introduction to Functional Analysis, Wiley, New York, 1958.
- [18] E. C. Titchmarsh, The Theory of Functions, Clarendon Press, Oxford, 1939.
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.baztech-692aac39-9308-4338-a706-ee96e1e977b6