Pole placement for l1-suboptimal design

In this paper we incorporate placement of one real closed loop pole into an l₁ controller design problem-that of designing a stabilising feedback compensator to minimise the l₁ norm of the tracking error when following a specified bounded command in a SISO discrete-time system. It is well known that the optimal solution to this problem involves a deadbeat closed loop map of finite, but possibly very high order, from command to tracking error. We show that for a class of plants, if the controller order is to be less than that required for the l₁-optimal solution, it is better to use closed loop pole locations other than deadbeat