Euler Discretization

Discretization of a continuous system, but does not need the same assumptions as Exact Discretization.

However, the plant using euler discretization might be unstable, even though the underlying plant is stable. Dependant on time steps.

Criterion for first order system - $|1+T\lambda |\le 1$

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$$\dot{x}[k]\approx \frac{x[k+1]-x[k]}{T}$$

$$\downarrow$$ $$x[k+1]=\mathbb{I}x[k]+TAx[k]+TBu[k]$$