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Weak condition for the existence of control sets with a nonempty interior of linear control systems on nilpotent groups

Adriano Da Silva, Anderson Felipe Penagos Rojas

Abstract

In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as the set of singularities of the drift is compact. Moreover, this control set is unique and contains the singularities of the drift in its closure.

Weak condition for the existence of control sets with a nonempty interior of linear control systems on nilpotent groups

Abstract

In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as the set of singularities of the drift is compact. Moreover, this control set is unique and contains the singularities of the drift in its closure.
Paper Structure (8 sections, 75 equations, 1 figure)

This paper contains 8 sections, 75 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Background
  3. Linear vector fields
  4. Linear control systems
  5. Control sets of LCSs
  6. The regular case
  7. The general case
  8. LCSs on the Heisenberg group

Figures (1)

  • Figure :