Controllability of Bilinear Systems: Lie Theory Approach and Control Sets on Projective Spaces

Oscar Raúl Condori Mamani (), Bartolome Valero Larico, María Luisa Torreblanca and Wolfgang Kliemann
Additional contact information
Oscar Raúl Condori Mamani: Facultad de Ciencias Naturales y Formales, Universidad Nacional de San Agustín de Arequipa, Arequipa 04001, Peru
Bartolome Valero Larico: Facultad de Ciencias Naturales y Formales, Universidad Nacional de San Agustín de Arequipa, Arequipa 04001, Peru
María Luisa Torreblanca: Facultad de Ciencias Naturales y Formales, Universidad Nacional de San Agustín de Arequipa, Arequipa 04001, Peru
Wolfgang Kliemann: Department of Mathematics, Iowa State University, Ames, IA 50011, USA

Mathematics, 2025, vol. 13, issue 14, 1-15

Abstract: Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists, for the induced system on projective space. We use the system semigroup by considering piecewise constant controls and use spectral properties to extend the result to bilinear systems in R d . The contribution of this paper highlights the relationship between all the existent control sets. We show that the controllability property of a bilinear system is equivalent to the existence and uniqueness of a control set of the projective system.

Keywords: bilinear control systems; Lie theory; control sets; homogeneous spaces; Lyapunov exponents; Floquet spectrum; linear control semigroups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/14/2273/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/14/2273/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:14:p:2273-:d:1701834

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().