L2-Sensitivity Minimization for MIMO Linear Discrete-Time Systems Subject to L2-Scaling Constraints

Abstract — We formulate the problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints 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. Next, an efficient quasi-Newton algorithm is applied with closed-form formula for gradient evaluation to solve the unconstrained optimization problem. The optimal system structure is then constructed by employing the resulting coor-dinate transformation matrix that minimizes the L2-sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique. I