Parametric eigenstructure assignment using state-derivative feedback for linear systems

This paper addresses a complete parametric approach for solving the eigenstructure assignment problem using state-derivative feedback for multivariable linear systems. In the present work, both linear control systems with nonsingular and singular open-loop state matrices are treated and the corresponding parametric expressions to the feedback gains are derived. The parametric expressions for gains describe the available degrees-of-freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms are utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrices is minimized. Finally, a vibration absorber system is introduced to demonstrate the effectiveness of the proposed solution.