A Note on Surgical Eigenstructure Assignment via State Feedback

TL;DR

This paper discusses how to assign eigenvalues and eigenvectors of a linear system using state feedback, clarifying conditions for full eigenstructure control and the ability to freely assign remaining eigenvalues.

Contribution

It provides clarification on eigenstructure assignment conditions and demonstrates that remaining eigenvalues can be freely assigned once key eigenvectors are specified.

Findings

Eigenvalues and eigenvectors can be assigned via state feedback under classical conditions.

Remaining eigenvalues are freely assignable once key eigenvectors are fixed.

The paper clarifies the relationship between eigenstructure assignment and classical controllability conditions.

Abstract

Assignability of all eigenvalues and a subset of key eigenvectors/generalized eigenvectors of a linear time-invariant system via state feedback is considered. We clarify that, if the key eigenvectors/generalized eigenvectors and their associated eigenvalues satisfy the classical conditions for full eigenstructure assignment, the remaining eigenvalues can be assigned at will.