Partial Eigenvalue Assignment for LTI Systems with $$\mathbb {D}$$ D -Stability and LMI

Abstract

Partial eigenvalue assignment (PEVA) is a milestone in the field of structural dynamics control, for which the system models based on finite-element analysis have larger dimensions. The solution for PEVA has early seminal contributions, but today, other relevant advances have been offered by researchers in this interdisciplinary field. This work aims to demonstrate the construction of a new method to solve PEVA in linear time-invariant systems to guarantee the regional stability of the reassigned eigenvalues. The theoretical review of PEVA and $$\mathbb {D}$$ -stability are shown to support the development of an algorithm that involves linear matrix inequalities and left-eigenvectors parametrization. To verify the efficiency of the algorithm, tests were performed on numerical examples borrowed from the literature. Furthermore, the solution’s quality is illustrated through location plots and eigenvalue comparison tables.