Robust model following control for a class of second-order dynamical systems subject to parameter uncertainties

A robust model following control for a class of second-order dynamical systems subject to parameter uncertainties is considered in this article. The problem is decomposed into two subproblems: a robust state feedback stabilization problem for second-order dynamical systems subject to parameter uncertainties and a robust compensation problem. The latter concerns solution of three coefficient matrices such that five matrix equations are met and, simultaneously the effect of the uncertainties to the tracking error is minimized. Based on a complete parametric solution to a class of the second-order generalized Sylvester matrix equations, the robust compensation problem is turned into a minimization problem with linear constraints. The set of linear equations is derived that determines the solution to the minimization problem. A numerical example is given to demonstrate the validity of the results.