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A projection algorithm for partial eigenvalue assignment problem using implicitly restarted Arnoldi method

The problem of reassigning a part of the open-loop spectrum of a linear system by feedback control, leaving the rest of the spectrum invariant, is called the partial eigenvalue assignment problem. In this paper, a projection method based on a direct use of the implicitly restarted Arnoldi method for the partial eigenvalue assignment problem in linear control systems is presented. The method is of interest in common situations where the system is very large and only a few of its eigenvalues need to be assigned. Numerical examples are given to display the performance and the accuracy of the proposed algorithm.