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A simple solution to the optimal eigenvalue assignment problem

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2 Author(s)
D. P. Iracleous ; Dept. of Electr. & Comput. Eng., Patras Univ., Greece ; A. T. Alexandridis

The problem of the optimal eigenvalue assignment for multi-input linear systems is considered. It is proven that for an n-order system with m independent inputs, the problem is split into the following two sequential stages. Initially, the n-m eigenvalues are assigned using an (n-m)-order system. This assignment is not constrained to satisfy optimality criteria. Next, an m-order system is used to assign the remaining m eigenvalues in such a way that linear quadratic optimal criteria are simultaneously satisfied. Therefore, the original n-order optimal eigenvalue assignment problem is reduced to an m-order optimal assignment problem. Moreover, the structure of the equivalent m-order system permits further simplifications which lead to solutions obtained by inspection

Published in:

IEEE Transactions on Automatic Control  (Volume:44 ,  Issue: 9 )