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GATE ECE 2009 | Question-18

Consider the system $\frac{d x}{d t}=A x+B u$ with $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}p \\ q\end{array}\right]$ where $p$ and $q$ are arbitrary real numbers. Which of the following statements about the controllability of the system is true ?

  1. The system is completely state controllable for any nonzero values of $p$ and $q$
  2. Only $p=0$ and $q=0$ result in controllability
  3. The system is uncontrollable for all values of $p$ and $q$
  4. We cannot conclude about controllability from the given data
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