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

2023/11/13 by Adriano Da Silva, Da Silva, Adriano, Anderson F. P. Rojas +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2311.07364

openalex publication_date 2023/11/13 · openalex created_date 2023/11/15 · openalex updated_date 2026/07/28

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.

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• A complete classification of control sets for singular linear control systems on the Heisenberg group

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