×
Nambu, Takao

Stabilization and decay of functionals for linear parabolic control systems. (English) Zbl 1141.93051

Proc. Japan Acad., Ser. A 84, No. 2, 19-24 (2008).
Summary: We construct a specific feedback control scheme for a class of linear parabolic systems such that some nontrivial linear functionals of the state decay faster than the state, while the state is stabilized. In particular, we raise a new question of pole allocation which is subject to constraint, and derive a necessary and sufficient condition: an essential extension of the well known result by W. M. Wonham (1967).

MSC:

93D15 Stabilization of systems by feedback
35B35 Stability in context of PDEs
93B52 Feedback control
93C05 Linear systems in control theory

Keywords:

linear parabolic systems; feedback stabilization; dynamic compensator
PDF BibTeX XML Cite
\textit{T. Nambu}, Proc. Japan Acad., Ser. A 84, No. 2, 19--24 (2008; Zbl 1141.93051)
Full Text: DOI Euclid
  • logo of hbz
  • logo of WorldCat

References:

[1] S. Agmon, Lectures on elliptic boundary value problems , D. Van Nostrand Co., Inc., Princeton, N.J., 1965. · Zbl 0142.37401
[2] R. F. Curtain, Finite-dimensional compensators for parabolic distributed systems with unbounded control and observation, SIAM J. Control Optim. 22 (1984), no. 2, 255-276. · Zbl 0542.93056
[3] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order , 2nd ed., Springer-Verlag, New York, 1983. · Zbl 0562.35001
[4] D. G. Luenberger, Observers for multivariable systems, IEEE Automatic Control AC-11 (1966), 190-197.
[5] T. Nambu, On stabilization of partial differential equations of parabolic type: boundary observation and feedback, Funkcial. Ekvac. 28 (1985), no. 3, 267-298. · Zbl 0614.93049
[6] T. Nambu, Stability enhancement of output for a class of linear parabolic systems, Proc. Roy. Soc. Edinburgh Sec. A 133A (2003), no. 1, 157-175. · Zbl 1049.93046
[7] T. Nambu, An \(L^{2}(\Omega)\)-based algebraic approach to boundary stabilization for linear parabolic systems, Quart. Appl. Math. 62 (2004), no. 4, 711-748. · Zbl 1140.93460
[8] T. Nambu, A new algebraic approach to stabilization for boundary control systems of parabolic type, J. Differential Equations 218 (2005), no. 1, 136-158. · Zbl 1109.93038
[9] Y. Sakawa, Feedback stabilization of linear diffusion systems, SIAM J. Control Optim. 21 (1983), no. 5, 667-676. · Zbl 0527.93050
[10] W. M. Wonham, On pole assignment in multi-input controllable linear systems, IEEE Trans. Automat. Control AC-12 (1967), 660-665.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.