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Summary: ON THE STABILITY OF THE HINIlUL DESIGNPROBLEM
U. A. Wolovich
Division of Engineeringand
Lefschetz Center for Dynamical Systems
Brown University
Providence, Rhode Island 02912
Abstract
'A necessary condition for obtaining stable
solutions t o t h e minimaldesignproblem is pre-
sented. The condition is shown t o be sufficient
for insuring the stability of solutions which
neednot be m i n i m a l . The results are basedon
the recently developed notion of minimal bases of
rational vector spaces, andanexample is employed
to illustrate and clarify the procedure.
Thc m i n i m a l designproblem (HDP) can be
s t a t e d as fofiows: G i v e n a pxm rational transfer
matrix, Tl(s) of rank p(< m)T and a pxq r a t i o n a l
transfer latrix, T2(s), find a (rorq) proper
rational transfer matrix, T(s) , ofminimal dynamic
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