Eigenvalue Assignment in Second order systems Using Sylvester equations: Approach

Elmer R. L. Villarreal, Andres O. Salazar, Thiago F. do Nascimento, Lucas D. da Silva, Walter M. Rodrigues


Second-order systems are those whose models can be written by a second-order differen-tial equation. That is, they are those that have two poles. The present article proposes an approach to solve the output feedback control with eigenvalues for second-order systems using Sylvester equa-tions. The matrices are prescribed in advance and depend greatly on the controllability conditions,being assigned the system’s observability eigenvalues. Furthermore, the real-value spectral decom-position T (λ) is explored to establish conditions so that the feedback gain matrices do not overflow over the eigenvalue assignment. However, it should be noted that the proposed algorithms may present complex computational problems. Two theorems were presented using Sylvester equations.The algorithms were implemented based on Sylvester equations, and examples were presented with their conclusions.


Sylvester equations;Eigenvalue assignment;Output feedback control;Second order system.

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DOI: https://doi.org/10.5540/03.2022.009.01.0249


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