Let us consider the following difference equation:

where *y* and *u* represent the output and input respectively.

Let us start from *y* (*k* + 1). We get *y* (*k*) using a delay element shown in Fig. 10.2.

**Fig. 10.2**

In Fig. 10.3, *x*_{1}(*k*) represents *y*(*k*). From Eq. (10.1) we get

**Fig. 10.3**

Figure 10.3 shows the block diagram of Eq. (10.3).

The state equation and output equation are

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