Optimization of multidimensional scalar and block state-space models

Necessary and sufficient conditions of optimizing 2D Roesser´s state-space models by using 1D optimization algorithms are proposed. The 2D optimizing algorithm based upon S.Y. Hwang´s (1977) approach is then given. In addition, the N-D equivalent invariant relation between N-D scalar and block state-space models is investigated. It is shown that under the criterion of minimizing the average output roundoff noise variance with the same dynamic range constraint, the extended block state-space model will be optimized, if the original scalar state-space model is optimized