Optimization of for loop to generate matrix

Hallo, I am solving a problem in model predictive control, where I need to create two new matrices H and S out of 3 given matrices A (diemension: 2x2), B (2x1) and C (1x2). Where

S=[C*A^9; C*A^9; …; C*A] (9x2)

and

H=[C*A^7*B C*A^8*B; C*A^7*B C*A^8*B; …; 0 C*B] (9x2).

Note that the size of the resulting matrices is given by other parameters. In order to accomplish the computation I used the following code:

T=0.1;                                      %sampling interval

A=[1 (1-exp(-T)); 0 exp(-T)];               %creating A,B,C
B=[(T-1+exp(-T)); (1-exp(-T))];
C=[1 0];

H=zeros(9,2);                               %defining H and S
S=zeros(9,2);
for kk=1:9                                  %for loop to fill H and S
  H(10-kk,:)=[C*(A^kk)];
  S(10-kk,:)=[C*A^(kk-2)*B C*A^(kk-1)*B];
end
S(9,1)=0;

This is working in this particular case. I started to wonder, however, if there is a more elegant way to do this. Firstly I would like to set all entries of the matrix H where kk-2<0 equal to zero and secondly I searched for a better way then using kk-10 in order to reverse the entries of the matrix when creating it.

I spent already quiet a while to search the web for some ideas. Maybe some of you have a hint for me.

Thank you! Florian

Answer 1

[Andrei Bobrov]

sh = arrayfun(@(ii)C*A^ii,(9:-1:0).','un',0)
H = cat(1,sh{1:end-1})
S0 = [cellfun(@(x)x*B,sh(2:end));0]
S = S0(bsxfun(@minus,(1:9)+1,(0:1)')')