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Some results on the behaviour of transfer functions at the right half plane

  • * Corresponding author: Bülent Nafi Örnek

    * Corresponding author: Bülent Nafi Örnek 
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  • In this paper, an inequality for a transfer function is obtained assuming that its residues at the poles located on the imaginary axis in the right half plane. In addition, the extremal function of the proposed inequality is obtained by performing sharpness analysis. To interpret the results of analyses in terms of control theory, root-locus curves are plotted. According to the results, marginally and asymptotically stable transfer functions can be determined using the obtained extremal function in the proposed theorem.

    Mathematics Subject Classification: Primary: 32A10, 32A05.


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  • Figure 1.  Root-locus curves for the transfer function $ H(s) = \sum\limits_{i = 1}^{n}\frac{\alpha _{i}}{s-s_{i}}+i\beta $. It is assumed that $ \alpha_{i} $'s equal to 1 and $ \beta $ is zero. The figures are presented for different $ n $ values: (a) $ n = 1 $, (b) $ n = 2 $, (c) $ n = 3 $, (d) $ n = 4 $

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