Hi all,

I'm doing research in mobile robotics, and I have very little knowledge

of control theory. However, I am currently trying to use feedback

controllers to guide the robot along a given trajectory. The trajectory

defines the position, velocity and accelerations in the coordinate space

x,y over time, and the robot expects translational and rotational

velocity commands.

I have tried different feedback controller designs, and they worked

really well:

These controllers seem to have nice theoretical properties, like

exponential convergence and Lyanpunov stability. But what happens if

such feedback controllers are executed in discretized time steps? Are

there stability properties or error bounds that apply in this case? Are

there general answers to this questions, or are they different for each

stability property, or even for each controller?

Thanks for any answers, references or other help

Boris