In this article, the problem of eigenstructure in descriptor matrix second-order linear systems using combined velocity and acceleration feedbacks is considered. This is promising for better applicability in many practical applications where the velocity and acceleration signals are easier to obtain than the proportional and velocity ones. First, the necessary and sufficient conditions which ensure solvability are derived. Then the parametric expressions of gain controller and eigenvector matrix are formulated. The proposed approach can offer all the degrees of freedom and has great potential in practical applications. The solution is general and can be applied when mass matrices that can be either singular or nonsingular. In this framework, infinite eigenvalues for descriptor systems are relocated by finite ones.

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