Optimal H2/l1 control: the SISO case

Considers the problem of minimizing the H₂-norm of the closed loop map while maintaining its l₁-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the l₁-constraint are established