scaling eigenvalues in matrix A (state space form)

Question

A have matrix A. The values and eigenvalues are:

1.0000    0.0500         0         0         0
     0    0.9248    0.2489         0         0
     0   -0.0179    0.9998         0         0
     0         0         0    1.0000         0
     0         0         0         0    1.0000

end

1.0000
0.9623 + 0.0551i
0.9623 - 0.0551i
1.0000
1.0000 

This matrix is matrix A for linear discrite time system in state space form:

x(k+1) = A*x(k) + B*u(k)
y(k) = C*x(k)

I use linear matrix inequality to design observer for state estimation. The problem is that my problem to solve is infeasible. However if I multiply the matrix A by 0.9 then eigenvalues are

0.9000
0.8660 + 0.0496i
0.8660 - 0.0496i
0.9000          
0.9000

No my problem is feasible. Can I scale matrix A? More precisely, can I scale eigenvalues in matrix A to obtain eigenvalues las then 1 ?