Approach to Partial Eigenvalue Assignment Using Sylvester Equation in System-Second Order

EasyChair Preprint 5129

Abstract

The paper considers an approach to partial eigenvalue assignment in second-order descriptor systems via proportional plus derivative plus output feedback controller. It is shown that the problem is closely related to a so-called second-order Sylvester matrix equation. This study presents an approach to partial the eigenstructure assignment for the descriptor system where an algorithm is presented for calculated the output feedback matrix by equation de Sylvester. Two complete parametric methods for the proposed approach to partial eigenstructure assignment problems are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions. The second one utilizes the system's factorization and allows the closed-loop eigenvalues to be set undetermined and sought via specific optimization procedures. The theorems are presented using the Sylvester equations. Two algorithms are implemented using the Sylvester equation, and examples are presented with their conclusions.

Keyphrases: Second-order system, Sylvester equation, descriptor system

@booklet{EasyChair:5129,
  author    = {Elmer Rolando Llanos Villarreal and Andrés Ortiz Salazar and Carlos Eduardo Trabuco Dórea and José Mário Araújo and Paulo Victor Fernandes Vieira},
  title     = {Approach to Partial Eigenvalue Assignment Using Sylvester Equation in System-Second Order},
  howpublished = {EasyChair Preprint 5129},
  year      = {EasyChair, 2021}}