Goodevening,
given this state-space dynamical system It's asked to show if exists an initial state x(0) for whitch the output is:
![A=[0,1;-4,4]](https://control.com/forums/data/attachments/0/375-c36b4cbd6b49ba435628c58a9d6acb0f.jpg "A=[0,1;-4,4]")
![B=[1,1;1,0]](https://control.com/forums/data/attachments/0/376-1e440235a74d96d411cb213faa756a76.jpg "B=[1,1;1,0]")
![C=[1, 0.5]](https://control.com/forums/data/attachments/0/377-bb8102b9dd03db686a6d92bd20dc237a.jpg "C=[1, 0.5]")
![D=[0, 2]](https://control.com/forums/data/attachments/0/378-ec502be0e21b897bf039d2ba1a7e9a7c.jpg "D=[0, 2]")
.
I think that a possible solution is:
where
is equal to:
![[e^{2t}-4te^{2t} , \frac{e^{2t}}{2}+2te^{2t}]](/forums/proxy.php?image=https%3A%2F%2Fwww.electroyou.it%2Fforum%2Flatexrender%2Fpictures%2Fx43b64da5a6de5eb1491c101d7b2889a1.png.pagespeed.ic.WNBnwJm-I9.png&hash=6c420125343e594311ff42aed7b97f4e)
So it should exist an initial state x(0) for whitch this equation is satisfied:
![2+e^{2t}=[e^{2t}-4te^{2t} , \frac{e^{2t}}{2}+2te^{2t}] \cdot [x_{1} ; x_{2}]](/forums/proxy.php?image=https%3A%2F%2Fwww.electroyou.it%2Fforum%2Flatexrender%2Fpictures%2Fxd285aa51d8e18a45678d59fd7acc3750.png.pagespeed.ic.4sNjA4uDS1.png&hash=10c4ea2681e8b1a22a2e10e2007af02e)
Solutions are:
but these two values are not constants (they depend from time t ) so it doesn't exists an initial state x(0) that gives that output.
What do you think ? thank you for you time .
given this state-space dynamical system It's asked to show if exists an initial state x(0) for whitch the output is:
.
I think that a possible solution is:
where
So it should exist an initial state x(0) for whitch this equation is satisfied:
Solutions are:
What do you think ? thank you for you time .
