Pole placement for l 1-suboptimal design

Abstract

In this paper we incorporate placement of one real closed loop pole into an l 1 controller design problem - that of designing a stabilising feedback compensator to minimise the l 1 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 l 1-optimal solution, it is better to use closed loop pole locations other than deadbeat.