Continuous-Time System:
a1 = 11, a0 = 20, b1 = 5, 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 = 6.67512, x(t) = 0
t = 6.67512, x(t) = -1
t = 7.3474, x(t) = -1
t = 7.3474, x(t) = 2
t = 7.54214, x(t) = 2
t = 7.54214, x(t) = -20
t = 7.65909, x(t) = -20
t = 7.65909, x(t) = 14
t = 8.3433, x(t) = 14
t = 8.3433, x(t) = 10
t = 8.63166, x(t) = 10
t = 8.63166, x(t) = 0
t = 14.8099, x(t) = 0

Discrete-Time System:
a0 = 10, a1 = 8, b0 = -11, b1 = -11, 
0 <= n < 6,  x[n] = 0
6 <= n < 7,  x[n] = -9
7 <= n < 11,  x[n] = -8
11 <= n < 14,  x[n] = 5
14 <= n < 30,  x[n] = 0

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