If you can't get access to the Control System Toolbox, you can manually perform spectral decomposition for a 2x2 matrix like H = [1 2; 2 -1] using basic MATLAB commands, since the spectral decomposition is essentially finding the eigenvalues and eigenvectors of the matrix.
H = [1 2; 2 -1];
% Compute the eigenvalues and eigenvectors
[V, D] = eig(H);
% V contains the eigenvectors, D contains the eigenvalues on the diagonal
% The columns of V are the eigenvectors and the diagonal elements of D are the corresponding eigenvalues
% The matrix G here is V, and S is D in the spectral decomposition formula H = V*D*V'
G = V;
S = D;
% Display the results
G, S
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