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Output stabilisation for a class of linear parabolic differential equations*

  • Takao Nambu (a1)
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.

Copyright
COPYRIGHT: © Royal Society of Edinburgh 1988
References
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2Kato, T.. Perturbation Theory for Linear Operators (New York: Springer, 1976).
3Nambu, T.. Feedback stabilization for distributed parameter systems of parabolic type. J. Differential Equations 33 (1979), 167–188.
4Nambu, T.. Feedback stabilization for distributed parameter systems of parabolic type, II. Arch. Rational Mech. Anal. 79 (1982), 241–259.
5Nambu, T., Rostamian, R. and Seidman, T. I.. Feedback stabilization of a marginally stable heat conduction problem. Appl. Anal. 24 (1987), 215–238.
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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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