By Ostergard P. R.
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Additional info for A 2-(22, 8, 4) Design Cannot Have a 2-(10, 4, 4) Subdesign
A 1 J or 0 1 0 0 0 0 0 0 -A 1 these l atter b l ocks corresponding to finite and infinite e lementary divisors of the s in gular penci l (F - AG ) = ( A - AI b i ) . The row dimension of the first diagonal b lock corresponds , in the case of exact numerical computati on , to the d imensi on of the control labl e subspace R i . As mentioned before , how ever , the advantage of this approach to det ermining c ontro l l ab i l i ty l i e s in the numer ical stab i l ity of the algori thm for computing the Kronecker canonical form in the presence of numerical rounding error ( W i lkinson , 1978 ; van Dooren , 1977 ) , us ing the s ingular value decomposition algorithm to provide an assess ment of numerical "rank " .
Then conclusions can be drawn on e . g . the possible control algorithms , sampl ing rates and resolution for DACs and ADC . 2 . IS 2 . 1 . Criteria for comparison For comparing the behaviour of different dis crete control systems we sha l l use the sum of the square errors at the sampl ing moments as a performance cr iter ion . u (k- 1 ) ] s k=O � (2 . 1) with y (k) , y ( k) , u (k) : set point , process s output and control variable on discrete time k. ��ny modified vers ions of this criterion do exist : they lead to different control para meters .
Journ . Math . Analys is Appl ic . 34 , 90ll3 . Verbruggen , H . ( 1 9 7 5 ) . Digitale rege l systemen . Delftse Universitaire Pers , Del ft ( in Dutch) . Luyben , W . (1973) . Parallel cascade con trol . Indust . Eng . Chem . Fund . g, 463467 . Meyer , C . , 'R. Wood , D . Seborg (1979 ) . Experimental evaluation of analyt ical and Smith-predictors for distillat ion column control . AIChE Journ . 2 5 , 2 4 -3 2 . Baet s , E . (1978 ) . Control software for a LS I -1 1 microprocessor . Thes is , State Univers ity of Ghent , Ghent ( in Dutch) .