engineering recuitment GATE ECE 2023-24 Test Series Control Systems State Space Analysis Controllability
Consider the system \(\frac{{dx}}{{dt}} = Ax + Bu\) with \(A = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right],B = \left[ {\begin{array}{*{20}{c}} p\\ q \end{array}} \right]\) and \(C = \left[ {\begin{array}{*{20}{c}} r&s \end{array}} \right]\) where p, q, r and s are arbitrary real numbers. Which of the following statements is / are true?
1
The system is completely state controllable for any non-zero values of p and q
2
The system is not observable for all the values of r and s
3
only p = 0 and q = 0 result in controllability
4
The system is observable only when r = 0 and s = 0