MATLAB minreal for stabilizing a control plan

Question

Having weighing matrices G and Rin using lqry

  [K,~,~] = lqry(mysys,G,Rin);

I got the following error:

  Error using ss/lqry (line 96)   The "lqry" 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 [C D;0 I]'*[Q N;N' R]*[C D;0 I] positive definite (use EIG to check positivity).

If I want to use minreal for stabilizing the plan, how should I modify G and Rin ?

  mysys=minreal(mysys);
  G=?????
  Rin=?????
  [K,~,~] = lqry(mysys,G,Rin);

Answer 1

If your state representation is nonminimal and after passing through minreal some of the states are removed, then your Q and if you are using N matrix needs to comply with the new size.

Say you have a 2x2 system. If you had initially 5 states and you would have a 5x5 Q matrix, 2x2 R matrix and if you are using 3x2 N matrix.

Then suppose two of these states are removed after minreal. In that case the Q matrix would be 3x3, ,if you are using, N must be 3x2 for the new system.