Frequency-weighted l2-sensitivity minimization for MIMO linear discrete-time systems subject to l2-scaling constraints

The minimization problem of a frequency-weighted l
2
-sensitivity measure subject to l
2
-scaling constraints for multi-input/multi-output (MIMO) linear discrete-time systems is formulated. An iterative technique is developed to solve the constrained optimization problem directly. The proposed solution method largely relies on the use of a Lagrange function, some matrix-theoretic techniques, and an efficient bisection method. A numerical example is presented to illustrate the utility of the proposed technique.