Two properties of l1-optimal controllers

The solution of the l₁ sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better-known H∞ sensitivity minimization problem or the LQG (linear quadratic Gaussian) problem is given of a one-parameter family of first-order plants where the order of the l₁-optimal compensator can be arbitrarily large, and thus it is impossible to bound the order of an l₁-optimal compensator in terms of the order of the plant. A plant is considered which has a continuous one-parameter family of l₁-optimal compensators, and thus l₁-optimal compensators need not be unique. The author´s two examples are considered to answer two questions left open by M.A. Daleh and J.B. Pearson (ibid., vol.32, p.314-23, 1987)