Adding matrix into bigger matrix iteratively-CodePudding

I'm trying to implement a matrix called Gamma in Matlab. It will include smaller matrices called H as seen in the figure below

I am having a trouble implementing this in Matlab.

What I have done is as follows:

I created a function called

function [Gamma] = get_Gamma(N,A,B,Cz)

then I create the H matrices

for i=1:N
   H(:,:,i) = Cz*Ad^(i-1)*Bd;
end

Hn = size(H,1);
Hm = size(H,2);

and my problem is how I can do iterations as this:

Gamma = [H(:,:,1) zeros(2,2)  zeros(2,2)]
Gamma = [Gamma  ; H(:,:,2)    H(:,:,1)    zeros(2,2)]
Gamma = [Gamma  ; H(:,:,3)    H(:,:,2)    H(:,:,1)]

I have been trying to do something like this

Gamma = [];

counter = 1;
for i=1:N
    for j=1:N
        if i <= counter
            Gamma_update = H(:,:,j);
            Gamma = [Gamma Gamma_update];
        else
            Gamma_update = zeros(Hn,Hm);
            Gamma = [Gamma Gamma_update];
        end

        Gamma = [Gamma ; H(:,:,2) H(:,:,1) zeros(2,2)]
    end
end

but I know this is not going to work. I hope you can help me out with this please!

CodePudding user response：

I just managed to find a solution to my problem and it is as follows:

function [Gamma] = get_Gamma(N,Ad,Bd,Czd)
% N: number of impulse response matrices to find Markov Parameters

for i=1:N
    H(:,:,i) = Czd*Ad^(i-1)*Bd;
end

Hn = size(H,1);
Hm = size(H,2);

Gamma = [];
counter = 1;

for i=1:N
    Gamma_update = [];
    for k=N:-1:counter 1
        Gamma_update = [zeros(Hn,Hm) Gamma_update];
    end
    for j=1:counter
        Gamma_update = [H(:,:,j) Gamma_update];
    end
    Gamma = [Gamma ; Gamma_update];
    counter = counter   1;
end

end