Response to an Input System

Hi to everyone, I have to deliver a very simple project in matlab, however i am a neophyte and despite the guides I can not find a correct solution.

I have to trace the response of a system to an input signal.

The system has the following matrix form:

A=[-1 0 2; 0 -2 1; 0 0 -3];
B=[0;1;0];
C=[1 -1 1];
D=[1];

The input signal is:

2*step(t) + ramp(t-5) + step(t-5) + ramp(t-7)

Now, I know the response to a generic input is:

lsim(sys,u,t)

The problem is that I can not correctly represent the various signals. For example, for the step starting at t = 0, I know it is represented in this way:

unitstep = t> = 0;

When I go to represent the ramp starting at t = 5, it is not represented correctly (I saw it through the plot).

Can anybody tell me how to represent the various signals properly and the sum of these?

Also I would like to know how to calculate the bandwidth of my system, as when I calculate it with "bandwidth", the result is "inf".

Thanks.