Let $A = [-1 0; 0 −2] , B = [ 0; 1] , C = [1; 0]^T , D = 0$ be a state space realization. Determine the transfer function. Determine the step response of the state from the variation of parameters formula and the output from the transfer function.
My problem is that transfer function is coming out to be zero. Can anyone sugges what to do next?
Do you understand why your transfer function is zero? Ever heard of controllability/observability of a system? In your case there is no eigenvalue of your $A$ matrix that is both controllable and observable. So your transfer function is bound to be zero. Whatever input you give to the system, you will see zero output. There is nothing you can do about it except change the system matrices.