ABSTRACT
In the preceding chapters on stabilization problems, we have constructed suitable feedback laws such that the state of the system decays with the designated decay rate as t → ∞ The outputs are (bounded or unbounded) linear functionals of the state. In this chapter, we focus our attention on stability enhancement of outputs and related linear functional for a class of linear parabolic systems by means of feedback control, and present sufficient conditions which turn out to be fairly different from those for regular state stabilization. Stability enhancement of outputs is regarded as “stabilization” of outputs to strengthen the stability property of outputs. Regular feedback laws are such that the state of the system strongly converge to zero as t → ∞ in respective topology of function spaces. Let H be a separable Hilbert space equipped with inner product ⟨·, ·⟩ H and norm ║·║ H . Let us consider the following control system with state u(·) in H: () d u d t + L u = ∑ k = 1 M f k ( t ) g k , u ( 0 ) = u 0 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367798/bad9a720-4aeb-4c28-9c18-ba1aa5ac9d9d/content/eq1960.tif"/>
