Robust Model Reference Control for Multivariable Linear Systems: A Parametric Approach

Abstract

The problem of robust model reference control for multi variable linear systems with structural parameter uncertainties is considered. It is shown that the problem can be decomposed into two sub-problems. One is a robust state feedback stabilization problem for multi variable linear systems subject to parameter uncertainties; the other is the so-called robust compensation problem which concerns solution of three coefficient matrices such that four matrix equations are met and the effect of the uncertainties to the tracking error is minimized simultaneously. Based on a complete parametric solution of a class of generalized Sylvester matrix equations, the robust compensation problem is turned into a minimization problem with a quadratic objective and a set of linear constraints.