MR2589659
Takao NAMBU
Takao NAMBU
On State and Output Stabilization of Linear Parabolic Systems
Funkcialaj Ekvacioj. Serio Internacia
52
2009
321--341
http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-3/52_321.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2589659
In feedback stabilization studies, a control scheme is designed so that the ``state'' of the system decays with a designated rate as $t\to\infty$. Thus the ``output'', which is subordinate to the state, also decays at least with the same rate. We study in the paper a class of linear parabolic systems, and construct a specific control scheme such that the output decays faster than the state.
Stabilization, Linear parabolic systems, Dynamic feedback scheme, Pole allocation subject to constraint, Dimension of a compensator.
Primary 93D15; Secondary 35B35, 35K50, 93C20.
52-321
2009
On State and Output Stabilization of Linear Parabolic Systems
Takao NAMBU
Takao NAMBU
1
Agmon, S.
Lectures on Elliptic Boundary Value Problems
Van Nostrand, Princeton
1965
MR0178246
2
Curtain, R. F.
Finite dimensional compensators for parabolic distributed systems with unbounded control and observation
SIAM J. Control Optim.
22
1984
255--276
MR0732427
3
Dunford, N.; Schwartz, J. T.
Linear Operators, Part III
Wiley Interscience, New York
1963
MR0412888
4
Fujiwara, D.
Concrete characterization of the domain of fractional powers of some elliptic differential operators of the second order
Proc. Japan Acad. Ser. A Math Sci.
43
1967
82--86
MR0216336
5
Gilbarg, D.; Trudinger, N. S.
Elliptic Partial Differential Equations of Second Order, 2nd ed.
Springer-Verlag, New York
1983
MR0737190
6
Grisvard, P.
Caractérisation de quelques espaces d'interpolation
Arch. Ration. Mech. Anal.
25
1967
40--63
MR0213864
7
Luenberger, D. G.
Observers for multivariable systems
IEEE Trans. Automat. Control
11
1966
190--197
8
Nambu, T.
On stabilization of partial differential equations of parabolic type: boundary observation and feedback
Funkcial. Ekvac.
28
1985
267--298
MR0852115
0852115
9
Nambu, T.
Stability enhancement of output for a class of linear parabolic systems
Proc. Roy. Soc. Edinburgh Sec. A
133
2003
157--175
MR1960053
10
Nambu, T.
An $L^2(\Omega)$-based algebraic approach to boundary stabilization for linear parabolic systems
Quart. Appl. Math.
62
2004
711--748
MR2104271
11
Nambu, T.
A new algebraic approach to stabilization for boundary control systems of parabolic type
J. Differential Equations
218
2005
136--158
MR2174970
12
Nambu, T.
Stabilization and decay of functionals for linear parabolic control systems
Proc. Japan Acad. Ser. A Math Sci.
84
2008
19--24
MR2386960
13
Sakawa, Y.
Feedback stabilization of linear diffusion systems
SIAM J. Control Optim.
21
1983
667--676
MR0710993
14
Weiss, G.; Curtain, R. F.
Dynamic stabilization of regular linear systems
IEEE Trans. Automat. Control
42
1997
4--21
MR1439361
15
Wonham, W. M.
On pole assignment in multi-input controllable linear systems
IEEE Trans. Automat. Control
12
1967
660--665