Exact pole assignment by output feedback Part 2

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Abstract
We continue the study in Fletcher and Magni (1987) concerning controllable and observable linear time-invariant multivariable control systems in which the number of inputs plus the number of outputs exceeds the number of states. In this paper we shall prove that exact assignment of distinct poles by means of a real output feedback is always possible if the set of poles to be assigned consists entirely of complex conjugate pairs of non-real numbers. We examine the problem of assigning these eigenvalues in complex conjugate pairs by means of the algorithm described in the first paper. We reduce the problem to the case in which just one of the observability and controllability indices of the system is larger than 2, and further detailed analysis then disposes of this case.

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