# Discretize a continuous LTI system: zero-order holding

08/11/2011

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

So

>>>

>>>

**2) Rigorous discrete system**

From

it is easy to see

>>>

>>>

Conclusion: Obviously, method 1 and 2 are equivalent to the first order!!!

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