Discrete Time

Info

Discrete means non-continuous or separate.

Controls Applications

Because physical plants are always Continuous Time systems, DT control systems are not digital control systems.

Stability

• Looking at a graph, if something looks like it grows exponentially fast based off of samples, it is clearly unstable

$\left|x[k]\right|=|\lambda {|}^k|x[0]|$:

• $\left|\lambda \right|<1$ ⇒ stable
• $\left|\lambda \right|>1$ ⇒ unstable
• $\left|\lambda \right|=1$ ⇒ unstable Basically, this relates to the unit circle where $|\lambda |$ is the bounds of the unit disk