It is often advantageous to work with discrete-time equivalent models of continuous-time systems, particularly with the advent of the digital computer. This section discusses only notation definition for state space models of discrete-time systems. The calculation of discrete-time models equivalent to continuous-time systems is discussed in Section 3.5.5.
The standard form for a time-invariant, discrete-time, state space model is
The above notation is equivalent to
Whenever possible, this topic will use the notation of eqns. (3.39-3.40) because it is more compact. If, however, the state space variable names have subscripts, it may be necessary to use the notation of eqns. (3.423.42). In either model format, it is understood that
where T is the time increment of the discrete-time system.
