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