A novel expression for L2 sensitivity evaluation in state-space digital filters and its minimization

This paper considers the problem of synthesizing the optimal finite-word-length state-space digital filter structures with minimum L ₂ sensitivity. First, the usual L₂ sensitivity measure is defined for state-space digital filters by using a pure L₂-norm. A novel expression is then developed for evaluating the L₂ sensitivity in state-space digital filters. Next, an iterative method is presented for obtaining the optimal coordinate transformation that minimizes the L₂ sensitivity measure. Applying the proposed method, the estimate at each iteration can be calculated analytically. In addition, this makes it possible to attain rapid convergence and high accuracy. Finally, a numerical example is given to illustrate the utility of the proposed method