Further results on rational approximations of L1-optimal controllers

When disturbances and outputs are persistent bounded signals, the worst case disturbance rejection problem leads to the L¹ optimal control theory. Recently, two rational approximations to the optimal L¹ controller were developed independently. We explore the connection between these approaches. The main results show that both belong to the same subset Ω of the set of admissible rational approximations. Additionally, by exploiting the structure of the dual to the L¹ optimal control problem we furnish a procedure to compute rational approximation with error smaller than a prespecified bound.