Robust and minimum norm stabilization for uncertain singular second-order vibration systems

In this paper, stabilization problems of uncertain singular second-order vibration systems are studied using eigenstructure assignment technique. The parametric design approach is presented using singular value decomposition method and characteristic relations of closed-loop uncertain systems. The condition number and sensitivity function are constructed to measure the robustness of uncertain closed-loop eigenvalues. A constructive method is proposed to optimize robust and minimum norm parameters simultaneously. The minimum norm solutions are calculated by solving corresponding optimization function. Algorithms are given for computing robust and minimum norm controller gains for uncertain singular second-order vibration systems. Numerical simulations are provided to verify the given results and methods.