\(\ell_1\)-suboptimal robust controller design for discrete linear SISO plants with structured uncertainty (Q1881905)

An \(\ell_1\)-optimal robust control design is studied for a discrete linear SISO plant with bounded additive disturbances and independent output and control operator perturbations. The existence of an \(\ell_1\)-optimal robust linear time-invariant controller is proved, and a design algorithm for a suboptimal controller with a rational transfer function is proposed. An algorithm for checking the robust stabilizability of the plant is presented, and a geometric interpretation is given for a number of optimal robust controller design problems known from the literature.