Cannot compute Riccati solution for LQI controller

Kshitij Singh answered . 2025-07-09 03:39:29

I suspect the issue is with stabilizability of the augmented system. Note that the code as posted is checking controllability of the plant, but the LQR solution requires stabilizability of the augmented plant, i.e., the plant combined with the integral control. I think the augmented system (not incuding the reference input) can be formed as

 

sysaugmented = series(SYS,ss(zeros(6),eye(6),eye(6),0)); % with SYS.c = eye(6)

Then the rank of the controllability matrix is

>> rank(ctrb(sysaugmented)) 

ans =

     9

So the augmented system is not controllable. The eigenvalues are:

>> eig(sysaugmented)

ans =

         0
         0
         0
         0
         0
         0
         0
         0
         0
   -0.6188
         0
         0

So at least two of the uncontrollable modes are on the imaginary axis, which (I think) means the augmented system is not stabilizable, which violates one of the conditions for the solution to exist as stated here:

doc lqi

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