Explicit Construction of Stabilizing Robust Avoidance Controllers for Linear Systems With Drift

We propose a constructive design method for linear systems with a nontrivial drift term, guaranteeing robust global asymptotic stability of the origin of the closed-loop system, as well as robust obstacle avoidance. To obtain discontinuous input actions, our controller is designed in the framework of hybrid systems. Using our proposed hybrid controller, we demonstrate that solutions do not enter a sphere, which we term an avoidance neighborhood, around specified isolated points. The constructive controller design methodology, as well as the closed-loop properties, is investigated via numerical examples.

Automated summary

The study introduces a design method for linear systems ensuring stability and obstacle avoidance, utilizing a hybrid controller design. The proposed controller successfully prevents solutions from entering a sphere around specified obstacle points.