Low-Parametric-Sensitivity Realizations With Relaxed $L_{2}$ -Dynamic-Range-Scaling Constraints

This brief presents a new dynamic-range scaling for the implementation of filters/controllers in state-space form. Relaxing the classical L ₂-scaling constraints by specific fixed-point considerations allows for a higher degree of freedom for the optimal L ₂-parametric sensitivity problem. However, overflows in the implementation are still prevented. The underlying constrained problem is converted into an unconstrained problem for which a solution can be provided. This leads to realizations that are still scaled but less sensitive.