The problem of minimizing a frequency-weighted l2-sensitivity measure subject to l2-scaling constraints is considered for multi-input/multi-output (MIMO) linear discretetime systems. The constrained optimization problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. An efficient quasi-Newton algorithm with closed-form formula for gradient evaluation is then applied to solve the unconstrained optimization problem. Finally, the optimal system structure is constructed by employing the resulting coordinate transformation matrix that minimizes the frequency-weighted l2-sensitivity measure subject to the scaling constraints. A numerical example is also presented to illustrate the utility of the proposed technique.

Keywords: MIMO linear discrete-time systems, Frequency-weighted l2-sensitivity.