Load Matching, Grid Interaction, and Advanced Control - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 322

(6.17)
where s is the complex frequency variable.
Equations (6.16) and (6.17) refer to a single-input, single-output (SISO).
Transfer functions can also be found between any pair of input and output
variables, either in multiple-input, single-output (MISO) systems, or in
multiple-input, multiple-output (MIMO) systems. An output of interest can
be found by using the transfer functions, relevant inputs, and the
application of the superposition principle ( Figure 6.10 ).
Fig. 6.10 Superposition principle in a MISO system with continuous-time
transfer functions
6.4.3.2 Discrete-Time Transfer Functions (Z-transforms Transfer
Functions)
Transfer functions in the Laplace domain provide insight on the dynamics
of the building (for example, simple periodic functions can be used to
represent weather variables). However, the input functions acting on a
building system are never “well-behaved” periodic functions, such as those
usually found in a Laplace transform table. In practice, modeling the
response of a building to actual inputs requires the use of z-transforms
transfer functions (Candanedo, 2011). These transforms are the
discrete-time counterpart of the Laplace transforms. They are more suitable
for inputs sampled at discrete time intervals. The z -transform of a sequence
is given by