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The transformation matrix W leading from (A, b) to theBF form can be computed as W = (Q)(QBF)-l, where Q B Fis the controllability matrix of (AB,, bBF)O. f course, thecontrollability matrices Q and QBF can be replaced withthe generalised controllability ones T and TB, , because,as can be seen from eqns. 4 and 5, the state transformationW modifies T according to the relation TBF =W-'T. Therefore we have
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