Time-varying optimal disturbance rejection in presence of plant uncertainty

The optimal robust disturbance rejection problem plays an important role in feedback control theory. Here its time-varying version is solved explicitly in terms of duality and operator theory. In particular, the optimum is shown to satisfy a time-varying all-pass property. Moreover, optimal performance is given in terms of the norm of a bilinear form. The latter depends on a lower triangular projection and a multiplication operator defined on special versions of spaces of compact operators.