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Necessary and sufficient conditions stability for n -input, n -output convolution feedback systems with a finite number of unstable poles

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2 Author(s)
Callier, F.M. ; Belgian National Fund for Scientific Research, Brussels, Belgium ; Desoer, C.A.

This paper considersn-input,n-output convolution feedback systems characterized byy = G astr eande = u - Fy, where the open-loop transfer functionhat{G}contains a finite number of unstable multiple poles andFis a constant nonsingular matrix. Theorem 1 gives necessary and sufficient conditions for stability. A basic device is the following: the principal part of the Laurent expansion ofhat{G}at the unstable poles is factored as a ratio of two right-coprime polynomial matrices. There are two necessary and sufficient conditions: the first is the usual infimum one, and the second is required to prevent the closed-loop transfer function from being unbounded in some small neighborhood of each open-loop unstable pole. The latter condition is given an interpretation in concepts of McMillan degree theory. The modification of the theorem for the discrete-time case is immediate.

Published in:

Automatic Control, IEEE Transactions on  (Volume:18 ,  Issue: 3 )

Date of Publication:

Jun 1973

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