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so in this example were going to go from the transfer function to controllable canonical form so a controllable canonical form were going to see that we have a specific representation for the system and we can identify that its in controllable canonical form by looking at the a and B matrices so heres our example transfer function G of s which is equal to Y of s over U of S is equal to s plus 3 over s cubed plus 9 s squared plus 24 s plus 20 so Im going to take this transfer function and now I can write Y of s is equal to s times X of s plus 3 times X of s because Im going to multiply the top and the bottom times the X of s so now that Ive done this I can see that U of S will be equal to s cubed times X of s plus 9 s squared times X of s plus 24 s times X of s plus 20 times X of s so now I can take the inverse Laplace transform of each of these and see that Y of T will be X dot of T plus three times X of T and U of T will be equal to the third derivative of X of T plus nine x d
