On frequency weighted minimal L/sub 2/ sensitivity of 2-D systems using Fornasini-Marchesini LSS model

The optimal state-space realization design problem is investigated in terms of minimizing a frequency weighted L/sub 2/-sensitivity measure for two-dimensional (2-D) linear digital systems represented with the Fornasini-Marchesini local state-space (LSS) model. An expression is derived for the transfer function error due to finite wordlength (FWL) effects on parameters. The optimal realization problem is then formulated, which is shown to be equivalent to minimizing the frequency weighted L/sub 2/-sensitivity measure. The problem is solved and the optimal design procedures are illustrated with an example.

[1]  Takao Hinamoto,et al.  Synthesis of 2-D state-space digital filters with low sensitivity based on the Fornasini-Marchesini model , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  M. Kawamata,et al.  Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems , 1990 .

[3]  Takao Hinamoto,et al.  Minimization of frequency-weighting sensitivity in 2 D systems based on the Fornasini-Marchesini second model , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  M. Gevers,et al.  Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects , 1993 .

[5]  Takao Hinamoto,et al.  Weighted sensitivity minimization synthesis of 2-D filter structures using the Fornasini-Marchesini second model , 1995, Proceedings of ISCAS'95 - International Symposium on Circuits and Systems.

[6]  R. Crochiere.  A new statistical approach to the coefficient word length problem for digital filters , 1975 .

[7]  Ali Zilouchian,et al.  A coefficient sensitivity bound in 2-D state-space digital filtering , 1986 .

[8]  M. Gevers,et al.  Parametrizations in control problems , 1993 .

[9]  Paul Moroney,et al.  The digital implementation of control compensators: The coefficient wordlength issue , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[10]  M. Gevers,et al.  Optimal synthetic FWI design of state-space digital filters , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[11]  Brian D. O. Anderson,et al.  Optimal FWL design of state-space digital systems with weighted sensitivity minimization and sparseness consideration , 1992 .

[12]  Lothar Thiele,et al.  On the sensitivity of linear state-space systems , 1986 .

[13]  Takao Hinamoto,et al.  Synthesis of 2-D state-space filter structures with low frequency-weighted sensitivity , 1992 .

[14]  V. Tavsanoglu,et al.  Optimal design of state - space digital filters by simultaneous minimization of sensitivity and roundoff noise , 1984 .