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The video tutorial explains the process of converting a transfer function to a controllable canonical form. By examining the A and B matrices, it is possible to identify if the system is in controllable canonical form. An example transfer function is given as G(s) = (s + 3)/(s^3 + 9s^2 + 24s + 20). By manipulating the transfer function, the system can be represented as Y(s) = sX(s) + 3X(s) and U(s) = s^3X(s) + 9s^2X(s) + 24sX(s) + 20X(s). Taking the inverse Laplace transform, Y(t) = X'(t) + 3X(t) and U(t) = X'''(t) + 9X'(t).
