Iteration of Matrix in equation

I am currently working on Model Predictive Control. In state prediction I have one equation x(k+i)=A*x(k+i-1)+B*u(k+i-1) where x,A,B & u all are matrices. I want to iterate this equation 'n' times. How to iterate equation in case of matrices?

Answer 1

[Babak]

Write a for loop and then iterate n times like this:

 n=5;
 number_of_states=12;
 A = ones(12,12);
 B = ones(12,1);

 x=zeros(12,n);
 u=zeros(12,n);  5 you need to know what the control effort vector is for all n

 for j=1:n
 x(:,j+1) = A*x(:,j)+B*u(:,j)
 end

then x(:,end) gives you the final state