How to remove LQR error ?

I am using LQR command in matlab for getting gain of matrix

A=[-1 1;0 2];
B=[1;0];
Q=[1 0;0 1];
R=[1];
k=lqr(A,B,Q,R)

I get error Like this

Error using lqr 
The "lqr" command failed to stabilize the plant or find an optimal feedback gain. To remedy
this problem:

1. Make sure that all unstable poles of A are controllable through B (use MINREAL to check)
2. Modify the weights Q and R to make [Q N;N' R] positive definite (use EIG to check positivity).

Is there any way to remove that error without using "minreal "command because if I use this then I am left with just 1 state(but I am using 5 states in my problem).I am changing my weights(Q and R by hit and trial method) as well to solve this problem but still fails.I will be very grateful to you if you help me out in this regard. is there any way of calculating Q and R weights for my matrix?

Can anyone help me in this regard.

[Bilal Karaki]

Because your system is not completely controllable.

Answer 1

[Azzi Abdelmalek]

Your model does not have 5 states (juste 2 states),one of them is not controllable. then you can't calculate the gain k by lqr method. The only way is to use minreal.

[sara]

This is not the actual problem.I have quoted this example because I am facing same problem as in that example.Actually my problem has 5 states and and out of them only 1 state is controllable but other states are not.If I use minreal command then I left with just one state only,then my problem is how to get responses of my other states?I actually want to get gain of other 4 states as well.I want to know that is there any other method for such case to calculate gain for all those states?Thats why I send this state space equation as an example.

[sara]

My problem is that I want to know any other method(means other than minreal command) to calculate gain for my system.

[sara]

I have to use other states as well in my coding and for that I want to know the gain(this is must).kindly send me answer on basis of above example so that I can solve my problem.

Answer 2

[Muhammad Ali]

"Minreal" command should solve your problem, because any of your state makes the plant uncontrollable.

[Azzi Abdelmalek]

That's what I said in the above answer

[Bilal sadiq]

sara is clearly asking that she/he has 5 states out of it only 1 state is controllable and obviously if she/he use minreal command it will return only 1 state then how one can apply lqr ?(or some other method) say for example

x1=translational displacement
x2=translational velocity
x3=angular position
x4=angular velocity
x5=actuator output

and suppose out of all these 5 state (after using minreal) we get only 1 state (say for example x2) then what should we do??? while our main objective was to control x3

hope you get what i am and sara suppose to ask