Question

The signal flow graph of a system is shown below:

The state variable representation of the system can be

• A. $\dot{x}=\left[\begin{array}{cc}1& 1\\ -1& 0\end{array}\right]x+\left[\begin{array}{c}0\\ 2\end{array}\right]u$
  
  $y=\left[\begin{array}{cc}0& 0.5\end{array}\right]x$
• B. $\dot{x}=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right]x+\left[\begin{array}{c}0\\ 2\end{array}\right]u$
  
  $y=\left[\begin{array}{cc}0& 0.5\end{array}\right]x$
• C. $\dot{x}=\left[\begin{array}{cc}1& 1\\ -1& 0\end{array}\right]x+\left[\begin{array}{c}0\\ 2\end{array}\right]u$
  
  $y=\left[\begin{array}{cc}0.5& 0.5\end{array}\right]x$
• D. $\dot{x}=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right]x+\left[\begin{array}{c}0\\ 2\end{array}\right]u$
  
  $y=\left[\begin{array}{cc}0.5& 0.5\end{array}\right]x$

Answer 1

The correct option is B $\dot{x}=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right]x+\left[\begin{array}{c}0\\ 2\end{array}\right]u$


$y=\left[\begin{array}{cc}0& 0.5\end{array}\right]x$
$\dot{x}=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right]x+\left[\begin{array}{c}0\\ 2\end{array}\right]u$

$y=\left[\begin{array}{cc}0& 0.5\end{array}\right]x$