Let us consider the following equation for 2nd order system:

In Eq. (10.6) there are two delay elements i.e., *y*(*k* + 2) and *y*(*k* + 1). Figure 10.4 shows the way of obtaining *y*(*k*) from *y*(*k* + 2).

**Fig. 10.4**

From Eq. (10.6) we can write

Let *x*_{1}(*k*) and *x*_{2}(*k*) be the output of delay elements of *x*_{1}(*k* + 1) and *x*_{2}(*k* + 1) respectively.

Figure. 10.5 shows the representation of Eq. (10.7).

**Fig. 10.5**

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