Exact pole assignment by output feedback Part 3

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Abstract
This part concludes a series of three papers concerning controllable and observable linear time-invariant multivariable control systems in which the number of outputs plus the number of inputs exceeds the number of states. Following from the second paper (Fletcher 1987) it remains to consider the assignment by real output feedback of a set of distinct eigenvalues consisting of a mixture of real numbers and complex conjugate pairs of non-real numbers. We examine the possibility that in the algorithm described in the first paper (Fletcher and Magni 1987) all the real eigenvalues can be assigned before any of the complex conjugate pairs. If this is possible then the argument of Fletcher (1987) can be used to complete the assignment. It is only from the failure of this possibility that the pathological cases detailed in the first paper can arise.