How to design the gain matrix for a set of desired closed loop poles?

You can use the PLACE function to adjust the gain matrix K. Please refer to the following documentation for more information:

https://www.matlabsolutions.com/documentation/control-system/place.php

Here's an example of the workflow:

A = [ 0   1   0010
     980  0  -2.8
      0   0  -10000100 ];

B = [ 0
      0
      100 ];

C = [ 1 0 0 ];

p1 = -10 + 10i;
p2 = -10 - 10i;
p3 = -50;

K = place(A,B,[p1 p2 p3]);
sys_cl = ss(A-B*K,B,C,0);