Robust asymptotic tracking in matrix second-order linear system

Robust asymptotic tracking problem of second-order system with structural parameter uncertainties is investigated directly in the matrix second-order linear system framework. It is shown that the problem can be decomposed into two parts, that is, the design problems of robust feedback stabilizing and feed-forward tracking compensation controller. Based on eigenstructure assignment approach and the model reference tracking theory, a parametric design approach for robust feedback stabilizing and feed-forward tracking compensation controllers is proposed in the matrix second order system framework, and insightful parameterizations of the closed loop eigenvalues sensitivities to the perturbed elements in the open loop system matrices are obtained. Based on the above methods, a simple and effective algorithm is then proposed. All the design degrees of freedom are used to optimize the controller through the algorithm. Its effectiveness is verified by an spacecraft rendezvous example.