The 'lsim' functon will work here. The code is correct and the input is getting applied only to the elevator (U3). If you are thinking why all the states are responding to only elevator input then this is expected because its a MIMO system and all the output states are coupled to each other. So basically there is no issue here.
However you can note a few minor things:
1) In this case you are checking open loop system response but I assume your next step will be to design a contoller here as the system is clearly unstable. Its always a good idea to let the plant settledown before applying any input in cases where you have some initial transient response. So in that case, after you define your input you can just make the input U3 zero for say 1 second before giving a step. Something like this:
u = [zeros(size(t)); zeros(size(t)); ones(size(t)); zeros(size(t));...
zeros(size(t)); zeros(size(t)); zeros(size(t))];
for i=1:127
u(3,i)=0;
end
2) Your state space system 'sys' is basically a 9x7 ss matrix depending on your number of inputs (7) and number of output state vectors (9). Now if you want to see impulse response of third input U3 to first state vector X1(Pitch rate) then just use:
3) You are already plotting the time response of first state vector (Pitch rate). I see no issue there.
