Electrical Circuits - Network/Transfer Function

[Victor Feitosa]

Homework Statement

The Matricial Circuit of a certain circuit in time-domain is:

[ -1 D+a] [v₁(t)] = [e_s(s)]
[D+2 -1] [v₂(t)] [0 ]

where a is constant >0.
Find G₁(s) = V₁(s)/E_s(s). Put your result in a relation of polinomials N(s)/D(s), with the D(s) monic polinomial

Homework Equations

The Attempt at a Solution

So, i tried to Laplace transform the matrix and then resolve the matrix equation, find V₁(s) and then put V₁(s)/E_s(s).
But D(s) is not a polinomial in this case. Am I missing something?
I think that there is a way to obtain D(s) but I'm not finding it. The book that I am using to study is Fundamental of Electrical Circuits 5th edition by Sadiku.

Thanks, guys!

 

[Victor Feitosa]

Ok, so this is my matrix equation in original post:

# \begin{pmatrix}
-1 & D+a \\
D+2 & -1
\end{pmatrix}
\quad
\begin{pmatrix}
v₁(t)\\
v₂(t)
\end{pmatrix}
\quad
=
\begin{pmatrix}
e_s(t)\\
0
\end{pmatrix}

 

[donpacino]

[ -1 D+a] [v1(t)] = [es(s)]
[D+2 -1] [v2(t)] [0 ]

is that supposed to be this?

[ -1 D+a] [v1(t)] = [es(s)]
[D+2 -1] [v2(t)]= [0 ]

if that is the case you should be able to use matrix algebra to solve for v1/es