Converting linear state space into a transfer function

[Std]

Homework Statement

Need elaboration in solving steps of...

Given The state space X(k)= [ 0.5 -0.5; 0.5 0.5] X(k-1) + [0;1] u(k) and out y(k) = [ 1 0] x(k) It is requested to get the tansfer function, Stability... and to design state feedback gain [k1 k2] to place the system poles at the origin....

Relevant Equations

transfer function is = C* [SI-A]-1 * B

My questions are now... Do the steps of converting this space to transfer function include any laplace ? or just we do get [SI-A]-1 and then transfer function is = C* [SI-A]-1 * B As [1 0] * [s-1/det -0.5/det ; 0.5/det s-0.5/det] * [0; 1] = -0.5/s^2+s+0.5 I mean do we need any laplace after that and if yes ?? Why and when shall we use it?? Also what is the difference in steps of solving if the question given was descriping the state as x' not x(k)?

How to get stability ... and feedback gain??

 

[scottdave]

I see this is a couple of months old. Where have these questions been? It also appears that @Std has been inactive since right after posting.

It has been awhile for me, so I'd have to look it up to get the steps to solve it. As I remember it, you should be able to stay in the s-domain solving for the poles and the gain, though. It's mostly algebra with the polynomials in s, if I remember correctly.