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Output stabilisation for a class of linear parabolic differential equations*

Published online by Cambridge University Press:  14 November 2011

Takao Nambu
Takao Nambu
Affiliation:
Department of Mathematics, Faculty of Engineering, Kumamoto University, Kumamoto 860, Japan.
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Synopsis

We study the output stabilisation for a class of linear parabolic differential equations in a Hilbert space by means of feedback controls. The output is given as a finite number of linear functionals. Stabilisationof the state, of course, implies stabilisation of the output. In the present paper, however, we give a sufficient condition (an algebraic condition on the above functionals) for the output stabilisation, which is weakerin some sense than that for the state stabilisation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 1-2 , 1988 , pp. 125 - 133
Copyright
Copyright © Royal Society of Edinburgh 1988

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References

1Gilbarg, D. and Trudinger, N. S.. Elliptic Partial Differential Equations of Second Order (New York: Springer, 1977).CrossRefGoogle Scholar
2Kato, T.. Perturbation Theory for Linear Operators (New York: Springer, 1976).Google Scholar
3Nambu, T.. Feedback stabilization for distributed parameter systems of parabolic type. J. Differential Equations 33 (1979), 167–188.CrossRefGoogle Scholar
4Nambu, T.. Feedback stabilization for distributed parameter systems of parabolic type, II. Arch. Rational Mech. Anal. 79 (1982), 241–259.CrossRefGoogle Scholar
5Nambu, T., Rostamian, R. and Seidman, T. I.. Feedback stabilization of a marginally stable heat conduction problem. Appl. Anal. 24 (1987), 215–238.CrossRefGoogle Scholar
6Sakawa, Y. and Matsushita, T.. Feedback stabilization of a class of distributed systems and construction of a state estimator. IEEE Trans. Automat. Control 20 (1975), 748–753.CrossRefGoogle Scholar
7Triggiani, R.. On the stabilizability problem in Banach space. J. Math. Anal. Appl. 52 (1975), 383–403.CrossRefGoogle Scholar
8Taylor, A. E.. Introduction to Functional Analysis (New York: John Wiley, 1958).Google Scholar
9Wonham, W. M.. On pole assignment in multi-input controllable linear systems. IEEE Trans. Automat. Control 12 (1967), 660–665.CrossRefGoogle Scholar