Abstract
This paper considers distributed n-input n-output convolution feedback systems characterized by y = G 1∗e , z = G 2∗y and e = u − z, where the forward path transfer function G ̂ 1 and the feedback path transfer function G ̂ 2 both contain a real single unstable pole at different locations. Theorem 1 gives necessary and sufficient conditions for both input-error and input-output stability. In addition to usual conditions that guarantee input-error stability a new condition is found which results in the fact that input-error stability will guarantee input-output stability. These conditions require to investigate only the open-loop characteristics. A basic device is the consideration of the residues of different transfer functions at the open-loop unstable poles. An example is given.
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