# Control system question

1. Apr 9, 2012

### erezb84

1. The problem statement, all variables and given/known data
I have the following matrix:
A=[0 -1; 0 -1]

and i need to calculate: exp(At) in several ways, 2 of them are using the reverse Laplace transform and using: I + Ʃ(A^kt^k)/k!

i have tried to start the series but i am getting an expression that i can't say which series it is,
and when i try with Laplace i get the one of the matrix expressions is a step function..

i will apreaciate the help...

thanks!

2. Apr 9, 2012

### RoshanBBQ

What are you getting for
$$(sI-A)^{-1}$$

3. Apr 9, 2012

### erezb84

this is what i get. but i can't find the reverse transform...

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4. Apr 9, 2012

### RoshanBBQ

You are dividing by the wrong thing. Divide by
$$s(s+1)$$
$$s(s+1)-1$$

5. Apr 9, 2012

### erezb84

but
$$s(s+1)-1$$
is the deteminante..
in oreder to reverse 2*2 matrix i do this:
[a b ; c d]^-1 = [d -b; -c a] * 1/det
no?

6. Apr 9, 2012

1*0 = 0

7. Apr 9, 2012

### erezb84

daaaam! right, thanks!