State derivative feedback in second-order linear systems: A comparative analysis of perturbed eigenvalues under coefficient variation

This paper presents a comparative study of sensitivity to parameter variation in two feedback techniques applied in second-order linear systems: state feedback technique and the less conventional state derivative feedback technique. The former uses information on displacements and velocities whereas the latter uses velocities and accelerations. Several contributions on the problem of partial or full eigenvalue/eigenstructure assignment using the state feedback technique are presented in the literature. Recently, some interesting possibilities, such as solving the regularization problem in singular mass second-order systems, are approached using state derivative feedback. In this work, a general equivalence between state feedback and state derivative feedback is first established. Then, figures of merit on the resulting perturbed spectrum are proposed in order to assess the sensitivity of the closed-loop system to variations on the system matrices. Numerical examples are presented to support the obtained results.