Work

Existence of eigensets for bilinear control systems

Year: 2025

Type: article

Abstract: For bilinear control systems in $ \mathbb{R}^d $, we prove under certain assumptions the existence of a nontrivial compact set $ D\subset\mathbb{R}^d $ satisfying $ \mathcal{O}_t(D) = e^{tR}D $ for all $ t>0 $, where $ R\in\mathbb{R} $ is a fixed constant and $ \mathcal{O}_t(D) $ denotes the orbit from $ D $ at time $ t $. This property generalizes the trajectory of an eigenvector in a linear dynamical system, and such a set merits the name 'eigenset'.

Source: Mathematical Control and Related Fields

DOI: 10.3934/mcrf.2025052

Author: Eduardo Celso Viscovini

Institution: Universidade Estadual de Maringá

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Award: G2823776494