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GATE 2020 EE – Question 48

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Multiple choice

The causal realization of a system transfer function $H(s)$ having poles at $(2,-1)$, $(-2,1)$ and zeroes at $(2,1)$, $(-2,-1)$ will be

  1. stable, real, allpass
  2. unstable, complex, allpass
  3. unstable, real, highpass
  4. stable, complex, lowpass

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Show answer and explanation

Correct answer: (B) unstable, complex, allpass

Explanation

The poles at $2-j$ and $-2+j$ are in both half planes, so the causal realization has a pole at $2-j$ in the right half plane and is unstable. The poles and zeros are not conjugate pairs of each other, so the coefficients are complex. Each zero is the negative of a pole, so the magnitude response is constant, i.e. the system is all-pass.