Approximation methods of mixed l1/H2 optimization problems for MIMO discrete-time systems

The mixed l
1
/H
2
optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l
1
-norm of a closed-loop transfer matrix while maintaining the H
2
-norm of another closed-loop transfer matrix at prescribed level. The continuity property ofthe optimal value in respect to changes in the H
2
-norm constraint is studied. The existence of the optimal solutions of mixed l
1
/H
2
problem is proved. Because the solution of the mixed l
1
/H
2
problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.