Solution of robust pole-placement problem via gradient flow

Abstract

This paper provides a computational procedure for a type of robust pole-placement problem. By exploiting the differentiability nature of the objective function based on the Frobenius norm condition number, the minimization problem is formulated in terms of a gradient flow to which standard ODE numerical routines can be applied. It is shown that a minimum point exists for the objective function. The algorithm is efficient and faces no singularity problem with the resulting eigenvector matrix. A numerical example is used to illustrate the technique and comparison to other methods is made.