Discretize a continuous LTI system: zero-order holding
The continuous LTI system is
The corresponding discrete system is
What are F and G? Usually we have two methods: use zero-order hold method to discretize it; or use approximation to a rigorous discrete system. Today I will show they are the same to the first order !!! So in the future, we are confident to directly use zero-order holding method to discretize a system as long as you want the first order accuracy!!!
1) Zero-order holding method:
where . Then
2) Rigorous discrete system
it is easy to see
Conclusion: Obviously, method 1 and 2 are equivalent to the first order!!!