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GATE 2020 BM – Question 20

Measurements and Control Systems · Control System Transfer Functions · 1 mark · Multiple choice

A state model is $\dot X=\begin{pmatrix}0&2\\a&0\end{pmatrix}X+\begin{pmatrix}b\\0\end{pmatrix}U$, $Y=(1\ 0)X$. Which condition makes it controllable?

  1. a=0,b≠0
  2. a≠0,b=0
  3. a≠0,b≠0
  4. a=0,b=0

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Show answer and explanation

Correct answer: (C) a≠0,b≠0

Explanation

The controllability matrix is [B AB]=[[b,0],[0,ab]]. Its determinant is ab². It has full rank precisely when both a and b are nonzero, C. The output equation does not affect controllability of the state pair (A,B).

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