Robust and Minimum Norm Optimization Method for Singular Vibration Systems with Time-Delay

There exist infinite eigenvalues in singular vibration systems, which give rise to unstable responses and poor performances. The stability of singular vibration systems can be changed by eigenstructure assignment method. In this paper, partial eigenstructure assignment problems (PESAPs) and robust and minimum norm partial eigenstructure assignment problems for singular vibration systems with time-delay are studied. A necessary and sufficient condition is derived to solve PESAPs for singular vibration systems with time-delay. The parametric solution for PESAPs is given by the Moore-Penrose pseudoinverse method, and the algorithm for solving PESAPs is proposed. An optimization algorithm is developed to solve robust and minimum norm PESAPs. The algorithm can obtain the three types of optimal solutions, which is applicable to singular and nonsingular vibration systems with time-delay. The effectiveness of the proposed algorithms is verified by the results of two numerical examples.