I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case.
For example, given the state-space equations of the second order, single input, single output discrete-time system:
$$ \begin{array}{lccrccr} \mathbf{x}[n+1] &=& \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} & \mathbf{x}[n] &+& \begin{bmatrix} b_{1} \\ b_{2} \end{bmatrix} & u[n] \\ y[n] &=& \begin{bmatrix} c_{1} & c_{2} \end{bmatrix} & \mathbf{x}[n] &+& d & u[n] \end{array} $$
How do I find the transfer function (i.e.; $H(z) = \dfrac{Y(z)}{U(z)}$) of this system?
As indicated on the Wikipedia article for the transfer function, the usual substitute for the Laplace transform for discrete time systems is the Z transform.