Partial eigenvalue assignment in linear time-invariant systems using state-derivative feedback and a left eigenvectors parametrization

Abstract

In this brief, a novel parametrized state-derivative feedback is given to achieve the well-known partial eigenvalue assignment in linear time-invariant systems. In particular, the parametrized matrix for linear feedback is shown to depend only on the measured (known) left eigenvectors and its corresponding eigenvalues that must be reassigned. The solution is proven to have no spillover, an appreciable feature for the cases in which most of the eigenstructure is unmeasured (unknown). Two numerical examples are given to see that the obtained formulas are valid for partial eigenvalue assignment using only measured information of the eigenstructure.