Mosek shows the result "Infeasible proble…", but the Primal residual is very small. I do not know what is trouble with my LMIs. Please help me.

[Zihao Cheng]

 yalmipversion: '20181012'

       yalmiptime: 0.6607

       solvertime: 0.3713

             info: 'Infeasible proble…'

          problem: 1

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

|    ID|          Constraint|   Primal residual|   Dual residual|

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

|    #1|   Matrix inequality|       -8.8889e-05|      5.8284e-06|

|    #2|   Matrix inequality|        8.8397e-55|          1.1568|

|    #3|   Matrix inequality|       -3.0737e-51|          1.5824|

|    #4|   Matrix inequality|       -2.5331e-51|          1.8391|

|    #5|   Matrix inequality|       -8.8889e-05|      5.8276e-06|

|    #6|   Matrix inequality|        8.6482e-55|          1.0612|

|    #7|   Matrix inequality|       -1.4948e-51|          1.4018|

|    #8|   Matrix inequality|       -2.8809e-51|           1.411|

|    #9|   Matrix inequality|       -2.2201e-51|         0.56932|

|   #10|   Matrix inequality|        4.6757e-55|          0.3152|

|   #11|   Matrix inequality|       -1.8617e-51|         0.56018|

|   #12|   Matrix inequality|       -3.5107e-51|         0.57175|

|   #13|   Matrix inequality|       -3.2368e-51|         0.55498|

|   #14|   Matrix inequality|       -2.8654e-51|         0.56506|

|   #15|   Matrix inequality|       -3.4722e-05|      4.0225e-06|

|   #16|   Matrix inequality|        6.2904e-54|         0.82982|

|   #17|   Matrix inequality|       -2.8776e-52|          1.2293|

|   #18|   Matrix inequality|       -2.7413e-52|          1.1944|

|   #19|   Matrix inequality|       -1.9035e-51|          4.5617|

|   #20|   Matrix inequality|       -1.7257e-51|          5.2878|

|   #21|   Matrix inequality|       -3.4722e-05|      4.0225e-06|

|   #22|   Matrix inequality|        3.3434e-54|          0.6638|

|   #23|   Matrix inequality|        1.4499e-51|         0.77541|

|   #24|   Matrix inequality|       -1.4327e-52|         0.74935|

|   #25|   Matrix inequality|       -2.6665e-51|          2.3837|

|   #26|   Matrix inequality|        1.3737e-52|          1.4972|

|   #27|   Matrix inequality|       -3.0006e-51|         0.39239|

|   #28|   Matrix inequality|        1.8139e-54|         0.15573|

|   #29|   Matrix inequality|       -9.5061e-52|         0.38276|

|   #30|   Matrix inequality|       -3.0844e-51|         0.44732|

|   #31|   Matrix inequality|       -2.4001e-51|         0.40389|

|   #32|   Matrix inequality|       -2.4561e-51|         0.45999|

[Zihao Cheng]

LFC_407_two_output.m  is the main programming. Sys_Para.m gives the system parameters. The LMIs are included in controller_SF.m.

[Johan Löfberg]

There is some bizarre numerical problem with your model, causing Mosek to generate a solution with non-sense small values. The first residual is significantly infeasible though

The fact that you have 10^-6 on the last diagonal element in e.g. LMI15, doesn't look like a good model to me. You are forcing that matrix to be psd, despite having such a small diagonal term

and already this small subset is infeasible

optimize(LMI([15 20]))