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The characteristic equation of a linear discrete-data control system is given as:
F(z) = z3 + z2 + z+ K = 0,
Where K is a real constant.
What is the range of values of K so that the system is stable?
  • a)
    0 < K < ∞
  • b)
    0< K< 1
  • c)
    —3 < K < ∞
  • d)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The characteristic equation of a linear discrete-data control system i...
Given, F(z) = z3 + z2 + z+ k =0
Using bilinear transformation, we put z = in the above characteristic equation.

or, (1 -K)r3 + (1 + 3K) r2 + 3(1 - K)r+ 3 + K = 0 Routh’s array is:

For the system to be stable, we have:
1 - K > 0 or K < 1    ...(i)
1 + 3 K > 0 or K  >     ...(ii)
3 + K > 0 or K > - 3    ..(iii)
From equation (i), (ii) and (iii) the range of values of K for stability is, 0 < K < 1.
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