MPC code efficiency, i would like to know the possibility of improving matrix multiplication efficiency

Say i have a controlable matrix of full rank A, i want to multiply this matrix in the form of [A,A^2,A^3,A^4........].

Here is my code

A=[0.7637 0.0873 0.0118 0.0003; -4.4281 0.6764 0.2214 0.0086; 0.4444 0.0159 0.9778 0.0621; 7.1286 0.4285 -0.3564 0.3449];

Dim=4;

N=1000000;%Horizon predicition

tic

%%Method1

Y=zeros(Dim*N,Dim);

for i=1:N

Y((i-1)*Dim+1:i*Dim,:)=A^i;

end

toc

%%Method2

tic

Y1=repmat(A,N,1);

for i=2:N

if(i<N)

Y1((i-1)*Dim+1:(i+1)*Dim,:)=repmat((mtimes(Y1((i-1)*Dim+1:i*Dim,:),A)),2,1);

elseif(i==N)

Y1((i-1)*Dim+1:(i)*Dim,:)=repmat((mtimes(Y1((i-1)*Dim+1:i*Dim,:),A)),1,1);

end

end

toc

The second method is much faster, i want to know the possibility of increasing the efficency, would some mathematical decomposition help here?