Eigenvalue/eigenvector assignment using output feedback

Abstract

The problem of pole-assignment in a linear time-invariant multivariable system using output feedback is considered. New sufficient conditions are derived to assign an almost arbitrary set of min <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n,m+r- 1)</tex> distinct eigenvalues, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> are the number of states, inputs, and outputs, respectively. The analysis also highlights the freedom in selection of closed-loop eigenvectors which can be used for response shaping.