Robust control against disturbance model uncertainty: a convex solution

The robust H
∞
-controller synthesis problem is considered for disturbances generated by an uncertain filter. The uncertainty in the filter is represented in the form of a linear fractional transformation, in which the uncertain element is assumed to satisfy a quadratic constraint. Solvability conditions are given in terms of linear matrix inequalities and it is shown how computational complexity can significantly be reduced by eliminating certain variables. The success of the developed synthesis procedure is illustrated by an example in which rejection of non-stationary sinusoidal disturbances is attained.