realization_matrix.m

matlab of linear system

D_bar0 = [2 0; 0 4]
D_bar1 = [5 0; 0 12]
D_bar2 = [2 0; 0 9]
D_bar3 = [0 0; 0 2]

N_bar0 = [-20 3; 2 1]
N_bar1 = [-2 6; 1 3]
N_bar2 = [4 0; 0 2]
N_bar3 = [0 0; 0 0]

Zero_block = [ 0 0; 0 0]

D_column = [D_bar0; D_bar1; D_bar2; D_bar3]
N_column = [N_bar0; N_bar1; N_bar2; N_bar3]

%there are deg*(p+q) column in total, and 2*deg*q rows in total
S = zeros(6*2,3*(2+2))

S(1:8,1:2) = D_column
S(1:8,3:4) = N_column
S(3:10,5:6) = D_column
S(3:10,7:8) = N_column
S(5:12,9:10) = D_column
S(5:12,11:12) = N_column

[Q, R] = qr(S)

S1 = S(1:10,1:8)
z2 = null(S1)
z2b = z2/z2(8)

S2 = S()