From the given state variable model of SISO it is possible to find its transfer function. Let the state variable model of the SISO be

The input vector for a SISO system has only one row and hence **U** (*k*) = *u*(*k*). Let us determine *H*(*z*). Taking *z* transform of Eq. (10.12) we get

i.e., (*z***I** − **A**) **X**(*z*) = *z***X** (0) **B***U*(*z*)

i.e., **X** (*z*) = (*z***I** − **A**)^{−1} *z***X** (0) + (*z***I** − **A**)^{−1} **B***U*(*z*) (10.14)

Taking **X** (0) as null matrix, we get from Eq. (10.14)

Taking *z*–transform of Eq. (10.13) we get

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