% Define symbolic variables

syms s

% Given transfer functions in G(s)

G11 = (2 * exp(-7*s)) / (10*s + 1)
G12 = (0.5 * exp(-4*s)) / (19*s + 1)
G21 = (exp(-3*s)) / (20*s + 1)
G22 = (1.5 * exp(-2*s)) / (15*s + 1)

% Calculating D12(s) as -G12(s) / G11(s)

D12 = -(G12 / G11);
D12 = simplify(D12);

% Display the results

disp('D12(s) =');
disp(D12);

% The presence of e^{-3s} indicates that the decoupler has a predictive capability – it can predict the future input change that affect the current output, i.e., the output change first before the input change (this can’t happen in our physical world). Therefore, the decoupler is considered a non-causal system, thus cannot be realized physically.
% Calculating D21(s) as -G21(s) / G22(s)

D21 = -(G21 / G22);
D21 = simplify(D21);

disp('D21(s) =');
disp(D21);

% Therefore, the decoupler is physically relizable, i.e., order of numerator is not higher than the order of denominator, and also there is no predictive term, only a delay term in the decoupler.
%