Tracking and Stabilization for Control Systems on Matrix Lie Groups

Abstract

A wide range of dynamical systems from fields as diverse as mechanics, electrical networks and molecular chemistry can be modeled by invariant systems on matrix Lie groups. This paper introduces control systems on matrix Lie groups and studies open- loop tracking and feedback stabilization for these systems in the presence of nonholonomic constraints. Using the concept of approximate inversion, results for drift-free, left-invariant systems on specific matrix Lie groups are presented.