STATE FEEDBACK LI-OPTIMAL CONTROLLERS CAN BE DYNAMIC

This paper considers l1-optimal control problems given by discrete-time systems with full state feedback, scalar control and scalar disturbance. Motivation stems from the central role that this problem structure played in the development of the H2 and H(infinity) theories. First, systems with a scalar regulated output are studied (singular problems). Sufficient conditions are given, based on the non-minimum phase zeros of the transfer function from the control to the regulated output, for the existence of a static l1-optimal controller. A simple way to compute the static gain is provided, using pole placement ideas. It is shown, however, that having full state information does not prevent the l1-optimal controller from being dynamic in general, and that examples with arbitrarily high order optimal controllers can be easily constructed. Second, problems with two regulated outputs, one of them being the scalar control, are considered (non-singular problems). It is shown, by means of a class ot fairly general examples for which exact e1-optimal solutions are constructed, that such problems may not have static controllers that are l1-optimal, thus concluding that a 'separation structure' does not occur in these problems in general.