Plotting step and impulse responses on Matlab

Question

I'm trying to graph a simple response function: 1/(1-0.5s^-1)

Now, I know that the function can also be written as: s/(s-0.5)

So I tried plotting the step and impulse responses in Matlab:

sys = tf([1 0],[1 -0.5])
figure(1);
step(sys);
figure(2);
impulse(sys);

And these are the graphs that I'm getting:

I think the shape of the step response is right; however, shouldn't the impulse response decay?

It just doesn't seem right that both graphs have the same shape.

Answer 1

Your system is unstable - the pole is in the right half s-plane.

Look at the vertical scales: \$10^{25}\$

If you want to get the step and impulse responses of an arbitrary, but stable, system try: \$sys=\small tf([1], [1\hspace{2mm} 1])\$

Answer 2

The system is unstable, the pole is in the rigth-half plane, then, the response increases exponentially.

Maybe you can try whit rlocus() function, to get another graphic representation.