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Simple solution to the optimal eigenvalue assignment problem
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DOI：10.1109/9.788545.png)
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Abstract
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The problem of the optimal eigenvalue assignment for multiinput linear systems is considered, It is proven that for an n-order system with 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.
Keywords:
eigenvalue assignment
linear systems
multivariable systems
optimal control
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