Mixed objective control synthesis: optimal l1/ℋ2 control

In this paper we consider the problem of minimizing the l₁ norm of the transfer function from the exogenous input to the regulated output over all internally stabilizing controllers while keeping its ℋ₂ norm under a specified level. The problem is analysed for the discrete-time, SISO, linear time invariant case. It is shown that an optimal solution always exists. Duality theory is employed to show that any optimal solution is a finite impulse response sequence and an a priori bound is given on its length. The problem is reduced to a finite dimensional convex optimization problem with an a priori determined dimension. Finally it is shown that, in the region of interest of the ℋ₂ constraint level the optimal is unique and continuous with respect to changes in the constraint level