Boundary feedback stabilization of a parabolic equation

  • Thomas I. Seidman
Session 7 Distributed Parameter Systems
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)


The equation (*) ut=uxx+qu+f will, in general, be unstable for positive q. We consider control through the boundary conditions u(·,0)=0, ux(·,1)=ф with observation available of φ :=3 u(·,1) and no knowledge of the initial state or of the input f. It is shown that one can construct a linear feedback law of the form (**) ф(t)=〈λ,φt〉+〈μ,фt〉 (фt, φt are intervals of past history) which stabilizes (*).


Parabolic Equation Boundary Control Unstable Mode Finite Order Quadrature Point 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Thomas I. Seidman
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Maryland Baltimore CountyBaltimoreU.S.A.

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