Business Question

Let we have the system as in the next form
�(�) = ��(�-1) + �(�-1)�(�-1), (1)
were
� =
⎝
⎜
⎛
0 � 0 … 0
0 0 � … 0
⋮ 0 ⋮ ⋱ ⋮
⋮ ⋮ ⋮ ⋱ ⋮
�(N-1) �(N-2) . . . B(1) �(0)⎠
⎟
⎞
∈ �!”×!”, (2)
�(�) = @
0
0
…
�(n)
C ∈ �!”×$, �(�) = @
�(� − � + 1)
�(� − � + 2)
…
�(�)
C ∈ �!”×”
with initial condition
�% =
⎝
⎜
⎛
0
0
…
0
�%⎠
⎟
⎞.
Suppose we know the x0 and the matrices B(n), and C(n).
Let we have B(n)= 1*n, and C(n)= 0.5*n, and x(0)=x0=0.1, so
1- Create a MATLAB function that calculate the A, and G(n) matrices as in (2) from the given
information.
2- If we let the input u is = linspace(-0.05, 0.05, 3)’ in the system (1).
Can we create a MATLAB code that solve or find all the outputs (z(1),….,z(N)) of system 1 by using
the previous matlab function. Not that the input u has 3 values at each step so want to have 3 values
for the output z in each step.
3- Again, let u is equal as in the previous and suppose we know z(N). Then, create a MATLAB
code that solve or find the outputs of system (1) backward by knowing z(N).