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The state variable representation of a system is given by:

The system is
  • a)
    neither controllable nor observable
  • b)
    controllable but not observable
  • c)
    uncontrollable but observable
  • d)
    both controiiabie and observable
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The state variable representation of a system is given by:The system i...

Here, 




So, IQCI = 0 - 0 + 2(0 - 4)
= - 8 ≠ 0
Hence, the system is controllable.
Also, Q0 = [CT ATCT (AT)2 CT]
Here,


and


So,

= 1 ≠ 0
Since |Q0| ≠ 0, therefore given system is observable.
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The state variable representation of a system is given by:The system isa)neither controllable nor observableb)controllable but not observablec)uncontrollable but observabled)both controiiabie and observableCorrect answer is option 'D'. Can you explain this answer?
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