Existence of eigensets on bilinear control systems

2024/09/17 by Eduardo C. Viscovini, Viscovini, Eduardo Celso
Computer Science · Engineering · #FOS: Mathematics #Mathematical Control Systems and Analysis #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2409.11194

openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For bilinear control systems in ℝ^d we prove, under an accessibility hypothesis, the existence of a nontrivial compact set D⊂ℝ^d satisfying O_t(D)=e^tRD for all t>0, where R∈ℝ is a fixed constant and O_t(D) denotes the orbit from D at time t. This property generalizes the trajectory of an eigenvector on a linear dynamical system, and merits such a set the name "eigenset".

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