A note on word length and memory requirements in digital control

It is shown that some of the parameters that result from identification and estimation algorithms of continuous time linear systems of order n, subjected to sampling and digital control, require about n binary bits to represent their integer parts. The storage space required for the integer parts of all such parameters is about n2/21n2. These estimates are approached in the case of fast sampling. The results are generalized to discrete time systems with poles confined to a circle of arbitrary radius. The need for developing structured algorithms is emphasized, since it is shown that the number of bits for the integer parts of these parameters could be reduced to just one bit and the storage space to about n binary locations, as a result of the structuring.