Discrete time models can be obtained directly from continuous time models, as summarized in this appendix. The MATLAB Control Toolbox can be used for these conversions, as shown in Module 4.
Consider a continuous state space model of the following form (where we have assumed D = 0)
A similar discrete state space model has the following form
Assuming that the sample time is Δt, and that the input u is held constant between time tk and tk+1, (A4.1) can be integrated to yield
which has the solution (although ...