Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization

The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semiinfinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l1-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations.