A direct algorithm for pole assignment of time-invariant multi-input linear systems using state feedback

Abstract A direct algorithm is suggested for the computation of the linear state feedback for multi-input systems such that the resultant closed-loop system matrix has specified eigenvalues. The extra freedom can be used in different ways, for example to decrease some norm of the feedback matrix or to improve the condition of some of the eigenvalues of the closed-loop matrix. The algorithm uses unitary transformations for numerical reliability, and is based on ideas from the QR algorithm for solving the eigenproblem. The stability of the algorithm is proven by doing a backward rounding error analysis, and numerical examples are given as well.

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