Continuous-Time System:
a1 = 12, a0 = 7, b1 = 8, b0 = 7, 

Your excitation signal x(t) consists of straight lines connecting these points.
It has been zero up until the first time and is zero after the last time.

t = 3.61294, x(t) = 0
t = 3.61294, x(t) = 11
t = 5.27772, x(t) = 11
t = 5.27772, x(t) = -3
t = 5.97577, x(t) = -3
t = 5.97577, x(t) = -8
t = 6.67792, x(t) = -8
t = 6.67792, x(t) = -6
t = 7.13038, x(t) = -6
t = 7.13038, x(t) = 1
t = 7.76179, x(t) = 1
t = 7.76179, x(t) = 0
t = 15.9223, x(t) = 0

Discrete-Time System:
a0 = 11, a1 = 8, b0 = -24, b1 = -11, 
0 <= n < 5,  x[n] = 0
5 <= n < 6,  x[n] = 20
6 <= n < 15,  x[n] = -8
15 <= n < 17,  x[n] = -5
17 <= n < 30,  x[n] = 0

x[n] has been zero up until the first time and is zero after the last time.