Abstract
In this paper, we shall deal with a linear control system ∑ defined on a Lie group G with Lie algebra L(G). We prove that, if G is a compact connected Lie group, then the vector fields associated to dynamic of ∑ are conservative, and that if G is also non-Abelian then, by using Poincare Theorem, ∑ is transitive if and only if it is controllable.
Keywords
Mathematics
Lie group
Simple Lie group
Pure mathematics
Abelian group
Adjoint representation
Lie algebra
Maximal torus
Discrete mathematics
Algebra over a field
Fundamental representation
Weight
Subject Areas
Advanced Topics in Algebra
·Algebra and Number Theory ·Physical Sciences
Stability and Controllability of Differential Equations
·Control and Systems Engineering ·Physical Sciences
Advanced Differential Equations and Dynamical Systems
·Geometry and Topology ·Physical Sciences