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Control Systems
State Variable Analysis
Controllability and Observability

Questions mapped to Controllability and Observability under State Variable Analysis.

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Q#1 State Variable Analysis GATE EE 2026 (Set 1) MCQ +2 marks -0.66 marks

A system is represented in state-space form as follows:

( : input,  : state vector,  : output)

Consider the new state vector

What is the state-space representation of the system in terms of the new state vector ?

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Q#2 State Variable Analysis GATE EE 2015 (Set 1) MCQ +2 marks -0.66 marks

In the signal flow diagram given in the figure,  are possible inputs whereas  are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

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When  is the only input and  is the only output.

When  is the only input and  is the only output.

When  is the only input and  is the only output.

When  is the only input and  is the only output.

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Q#3 State Variable Analysis GATE EE 2014 (Set 2) MCQ +2 marks -0.66 marks

The second order dynamic system         

has the matrices P, Q and R as follows:

The system has the following controllability and observability properties.

Controllable and observable

Not Controllable but observable

Controllable but not observable

Not Controllable and not observable

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Q#4 State Variable Analysis GATE EE 2013 (Set 1) MCQ +2 marks -0.66 marks

The state variable formulation of a system is given as

, , and

The system is

Controllable but not observable

Not controllable but observable

Both controllable and observable

Both not controllable and not observable

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Q#5 State Variable Analysis GATE EE 2012 (Set 1) MCQ +2 marks -0.66 marks

The state variable description of an LTI system is given by  

Where y is the output and u is the input. The system is controllable for

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Q#6 State Variable Analysis GATE EE 2002 (Set 1) MCQ +2 marks -0.66 marks

For the system, which of the following statements is true?  

The system is controllable but unstable

The system is uncontrollable and unstable

The system is controllable but stable

The system is uncontrollable but stable

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Q#7 State Variable Analysis GATE EE 1993 (Set 1) MCQ +1 mark -0.33 marks

Consider a second order system whose state space representation is of the form

If , then system is

controllable

uncontrollable

observable

unstable

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