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GATE 2014 EC (EC2) – Question 58

Control Systems · State Variable Model and Solution of State Equation · 2 marks · Multiple choice

For the state-space system represented by the signal-flow diagram, which property always holds?

Diagram for GATE 2014 EC (EC2) question 58
  1. Controllable
  2. Observable
  3. Stable
  4. Unstable

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Correct answer: (A) Controllable

Explanation

The integrator chain has x1′=x2,x2′=x3,x3′=a1x1+a2x2+a3x3+u. Thus B=(0,0,1) and the controllability matrix has determinant−1 regardless of a1,a2,a3. This is a controllable canonical realization, so it is **always controllable,A**. Arbitrary output coefficients can destroy observability, and arbitrary feedback coefficients need not yield stability.