Consider the two first-order controllable and observable subsystems \dot{x}_{1}(t)=a_{1} x_{1}(t)+u(t) \dot{x}_{2}(t)=a_{2} x_{2}(t)+u(t) If they are hooked in parallel such that y = x, – 2x,, what are the conditions required for the overall system to be both observable and controllable?

Fig: 1

Fig: 2

Fig: 3

Fig: 4