MIXED OBJECTIVE CONTROL SYNTHESIS - OPTIMAL L(1) H-2 CONTROL/

In this paper me consider the problem of minimizing the l(1) norm of t he transfer function from the exogenous input to the regulated output over all internally stabilizing controllers while keeping its H-2 norm under a specified level. The problem is analyzed for the discrete-tim e, single-input single-output (SISO), linear-time invariant case. It i s shown that an optimal solution always exists. Duality theory is empl oyed to show that any optimal solution is a finite impulse response se quence, and an a priori bound is given on its length. Thus, the proble m can be reduced to a finite-dimensional convex optimization problem w ith an a priori determined dimension. Finally, it is shown that, in th e region of interest of the H-2 constraint level, the optimal is uniqu e and continuous with respect to changes in the constraint level.