Robust Solution for Second-Order Systems Using Displacement–Acceleration Feedback

This paper addresses the robust and minimum norm controller design for matrix second-order linear systems by means of combined displacement and acceleration feedback. First, the necessary conditions that ensure solvability are presented. Then, the parametric expressions of gain controller and eigenvector matrix are formulated on the basis of a set of free parameters. The proposed solution simultaneously makes the resulting closed-loop system numerically robust and obtains gain controllers with minimum norms. Also, the solution is general and can be applied when mass matrices are either singular or nonsingular. This is promising for better applicability in many practical applications. Finally, two examples are provided to illustrate the effectiveness of the proposed control strategy.