Minimization of frequency-weighted l2-sensitivity subject to l2-scaling constraints for MIMO linear discrete-time systems using quasi-Newton algorithm

The problem of minimizing a frequency-weighted l₂-sensitivity measure subject to l₂-scaling constraints is considered for multi-input/multi-output (MIMO) linear discrete-time 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.