Robust model reference control for multivariable linear systems subject to parameter uncertainties

Robust model reference control for multivariable linear systems with structural parameter uncertainties is considered. It is shown that the problem can be decomposed into two subproblems: a robust state feedback stabilization problem for multivariable linear systems subject to parameter uncertainties and a robust compensation problem. The latter concerns solution of three coefficient matrices such that four 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 generalized Sylvester matrix equations, the robust compensation problem is turned into a minimization problem with quadratic cost and linear constraints. A set of linear equations is derived that determines the optimal solution to the minimization. An example illustrates the application of the proposed approach.