The electrical system shown in figure, converts input source current...
Given circuit is shown below,
Assume, iL(t) = x1 → First state variable
VC (t) = x2 → Second state variable
is (t) = u → Input of system
and V0 (t) = y → Output of system
Apply KCL at node N,
KVL in the loop between inductor and resistor,
From equation (i), (ii) and (iii), state variable modal can be written as,
Thus matrices A, B, and C are,
Condition of controllability,
Thus, system is uncontrollable.
Condition of observability,
Thus, system is un-observable.
So, the system is neither controllable nor observable.
Hence, the correct option is (D).