Boundary feedback stabilization of a parabolic equation
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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 (*).
KeywordsParabolic Equation Boundary Control Unstable Mode Finite Order Quadrature Point
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