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

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Julia Hariharan
Julia Hariharan 2020-12-7
回答： Walter Roberson 2020-12-7
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)

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回答（1 个）

Walter Roberson
Walter Roberson 2020-12-7
Your code does not have transpose(C)*C. It has C*transpose(C)

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