Abstract
Abstract This article considers the stability of n-input-n-output, linear time invariant convolution feedback systems. Stability theorems are expressed in terms of the Nyquist plots of the eigenvalues of Gcirc(s) where s varies along the Nyquist contour in the complex plane and Ĝ(s) is the transfer function of the open loop system which is allowed to have poles in the right half plane. Our objectives are to state clearly these theorems and to prove them. The paper investigates the geometry of the eigenvalues in the complex plane; in particular, the properties of the eigenvalues on and near the exceptional points, and the graph theoretic properties of the loci of the eigenvalues are studied. The stability theorems are proved using these geometric properties.
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