A direct algorithm for pole assignment of time invariant linear systems using output feedback

A direct algorithm is suggested for the computation of the linear output feedback for multi-input (m), multi-output (p) systems such that max{m,p} of the eigenvalues of the resultant closed-loop matrix have specified values. The extra freedom can be used in different ways, for example to decrease the Frobenious norm of the feedback matrix. All the transformations used are unitary, for numerical reliability, and the technique is based on ideas from the QR algorithm for solving the eigenproblem. The numerical stability of the algorithm is proven by doing the backwards rounding error analysis of it.