Linear control systems on Lie groups: null controllability

• Grant number: 09/08739-0
• Support type: Regular Research Grants
• Duration: August 01, 2009 - July 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: Eyüp Kizil
• Grantee: Eyüp Kizil
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

A class of linear control systems on Lie groups, introduced by Ayala-Tirao, is a natural generalization of classical linear systems on Euclidean space. In this project, we deal with null controllability property of linear control systems on specific Lie groups, and its extensions. More precisely, we are interested in establishing (globally) null controllability of a linear control system on a simply connected and nilpotent Lie group. For it, we assume that the system under consideration is locally controllable. The hypothesis that the spectrum of a derivation which produce the drift vector field of the system belongs to the complex semi-plane is indespensable to obtain such a result, which also occurs in the linear case. However, it is of our interest to obtain a stronger result in the sense that the stability condition is no longer needed. This will be studied for non compatc semi-simple Lie groups. The motivation is that such Lie groups admit so-called Iwasawa decompositions which appereantly implies that null controllability of an invariant control system can be reduced to that of the induced system on solvable component of the group. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VÍCTOR AYALA; EYÜP KIZIL. Null controllability on Lie groups. Proyecciones, v. 32, n. 1, p. 61-72, Mar. 2013.