**Example 10.9** Find the SV model for the system with

**Solution**

The given transfer function is

i.e., (*z*^{4} + 2*z*^{3} + 5*z*^{2} + 6*z* + 3) *Y*(*z*) = *U*(*z*)

i.e., *z*^{4}*Y*(*z*) + 2*z*^{3}*Y*(*z*) + 5*z*^{2}*Y*(*z*) + 6*z**Y*(*z*) = *U*(*z*) (1)

The inverse transform of Eq. (1) gives

i.e., *y*(*k* + 4) = *u(k)* − 2*y*(*k* + 3) − 5*y*(*k* + 2) − 6*y*(*k* + 1) − 3*y* (*k*)

Using four delay elements *y*(*k* + 3), *y*(*k* + 2), *y*(*k* + 1) and *y*(*k*), we can get *y*(*k* + 4) which has been shown in Fig. E10.6.

**Fig. ...**

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