Chain Controllability of Linear Control Systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 19 Aug 2024Embargo end date: 01 Jan 2023 Germany English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control and Optimization, volume 62, pages 2,387-2,411 (issn: 0363-0129, eissn: 1095-7138,

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Authors: Fritz Colonius; Alexandre J. Santana; Eduardo C. Viscovini;

doi: 10.1137/23m1626347 , 10.48550/arxiv.2312.14595

arXiv: 2312.14595

Chain Controllability of Linear Control Systems

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Abstract

For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals the sum of the control set around the origin and the center Lyapunov space of the homogeneous part. For the proof, the linear control system is extended to a bilinear control system on an augmented state space. This system induces a control system on projective space. For the associated control flow attractor-repeller decompositions are used to show that the control system on projective space has a unique chain control set that is not contained in the equator. It is given by the image of the chain control set of the original linear control system.

24 pages

Country

Germany

Related Organizations

Universität Augsburg
Germany
State University of Maringa
Brazil

Keywords

Controllability, attractor, 93B045, 37B20, Linear systems in control theory, Optimization and Control (math.OC), Poincaré sphere, Optimization and Control, FOS: Mathematics, linear control system, chain control set

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