engineering recuitment GATE IN Test Series 2023-24 Mock Test Control Systems State Space Analysis Controllability
The second order dynamic system
\(\frac{{dx}}{{dt}} = Px + Qu\)
y = Rx
has the matrices, P, Q and R as follows:
\(P = \left[ {\begin{array}{*{20}{c}} { - 1}&1\\ 0&{ - 3} \end{array}} \right]\;Q = \left[ {\begin{array}{*{20}{c}} 0\\ 1 \end{array}} \right]\;R = \left[ {0\;1} \right]\)
The system has the following controllability and observability properties:1
Controllable and observable
2
Not controllable but observable
3
Controllable but not observable
4
Not controllable and not observable