State-Space Digital Filters with Minimum Weighted Round-off Noise and Pole Sensitivity Subject to $\pmb{l}_{2}$ -Scaling Constraints

In this paper, we investigate the problem of minimizing roundoff noise and pole sensitivity simultaneously subject to l₂-scaling constraints for state-space digital filters. A measure for evaluating roundoff noise and pole sensitivity is introduced. An efficient iterative technique for minimizing this measure is then explored by relaxing the constraints into a single constraint on matrix trace and solving the relaxed problem with an effective matrix iteration scheme. Finally, the validity and effectiveness of the proposed technique is demonstrated by a numerical example.