Optimal pole placement in an l1 framework

We present results on the incorporation of two poles into the solution of l₁ optimisation problems where the solution order is constrained to be less than that for the true optimum. For a given order of solution, using two poles can allow a smaller l₁ norm to be obtained than can be obtained with a truncated polynomial solution, or a solution with just one real pole. Linear programs achieving pole placement for two distinct poles are presented, along with some applications of duality theory to obtain pole locations for a simple problem involving a complex pair of poles