The celebrated 1967 pole assignment theory of W. M. Wonham for linear finite-dimensional control systems has been applied to various stabilization problems both of finite and infinite dimension. Besides existing approaches developed so far, we propose a new approach to feedback stabilization of linear systems, which leads to a clearer and more explicit construction of a feedback scheme.
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The paper studies the stabilization problem for a class of linear parabolic boundary control systems with a Riesz basis. The author earlier proposed two different feedback control schemes to cope with the difficulties arising from the feedback terms on the boundary; these schemes are based on different ideas, and look fairly different from each other. We show, however, that they are algebraically similar.
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