Wong Chia-ho. Extended Graphical Representation of Rational Fractions with Applications to Cybernetics[J]. Applied Mathematics and Mechanics, 1981, 2(4): 387-396.
 Citation: Wong Chia-ho. Extended Graphical Representation of Rational Fractions with Applications to Cybernetics[J]. Applied Mathematics and Mechanics, 1981, 2(4): 387-396.

# Extended Graphical Representation of Rational Fractions with Applications to Cybernetics

• Publish Date: 1981-08-15
• In this paper, we discuss the extended graphical frepresentation of the fraction of a complex variable s

Where K is confined to be real. Three figures of the above fraction can be used in feedback systems as well as to study the properties of figures for any one coefficient of a characteristic equation as a real parameter. It is easy to prove the following theorem:
K1=f(n)(s)/(F)(d)(s),and K2=F(d)(s)/f(n)(s)
have the same root locus.By this graphical theory, we find out that if the zeros and poles of a fraction are alternatively placed on the axis x, then there is no complex root locus of this fraction, therefore the state of such a system is always non-oscillatory; Using these figures of this fraction, we can discuss its stable interval systematically.
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