Getting the error "In the "lyap(A,Q,...)" command, A and Q must be square matrices of the same size." even though my A and Q matrix are the same size

So, I am trying to find the observability Gramian of a system using the 'lyap' function in MatLab. My code works for my controllability Gramian but not the observability. I have checked my inputs for my 'A' and 'Q' matricies (in my code they are called 'transpose(A)' and 'transpose(C)*C) and they are both 3x3 matricies and yet I am getting this error. I have copied my code below, if anyone has any ideas please let me know - thank you!

clc;

A = [-3 1 1;0 -2 1; 0 0 -1];

B = [2;2;1];

C = [1 -1 0];

% compute the controllability matrix

C_mat = ctrb(A,B);

%let's see if the system is controllable

if(length(A)==rank(C_mat))

fprintf('Controllable\n');

else

fprintf('System is not controllable\n');

end

% Compute controllable subspace

[~,new] = rref(C_mat);

disp('The controllable subspace is:')

C_subspace = C_mat(:, new)

% compute the observability matrix

O_mat = obsv(A,C);

%let's see if the system is controllable

if(length(A)==rank(O_mat))

fprintf('Observable\n');

else

fprintf('System is not observable\n');

end

% Compute controllable subspace

[~,new] = rref(O_mat);

disp('The observable subspace is:')

O_subspace = O_mat(new, :)

%%%Part B%%%

%Controllability Gramian

% C_gram=(-B*transpose(B))/(A+transpose(A))

C_gram=lyap(transpose(A),-B*transpose(B))

%Test if CG is nonsingular i.e. det = 0

det(C_gram) %matrix is singular

%Observability Gramian

O_gram=lyap(transpose(A),-C*transpose(C))

%Test if OG is nonsingluar

det(O_gram) %matrix is nonsingluar

%%%Part C%%%

null(O_gram)

Answer 1

[Walter Roberson]

Your code does not have transpose(C)*C. It has C*transpose(C)