Abstract
In this paper, we explore an approach to check the exponential stability of the distributed parameter system with non-collocated feedback. We regard the characteristic determinant as an entire function with parameters that usually are the feedback gains. By checking that there is no zero of this entire function on the imaginary axis for some parameters, we assert that there is no spectrum of the system in the closed right half-plane. Further, we check the Riesz basis property of the eigenvectors of the system, and hence get the exponential stability of the system. As an example, we study a hybrid system consisting of onedimensional wave equation with tip mass and non-collocated feedback. By finding out the condition of no spectrum on the imaginary axis, we determine the exponential stability region of the parameters of the hybrid system.
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