- Title
- On feedback stabilisation of switched discrete-time systems via Lie-algebraic techniques
- Creator
- Haimovich, Hernan; Braslavsky, Julio H.; Felicioni, Flavia
- Relation
- 48th IEEE Conference on Decision and Control, 2009 held jointly with the 28th Chinese Control Conference, 2009 (CDC/CCC 2009). Proceedings of the 48th IEEE Conference on Decision and Control 2009, held jointly with the 28th Chinese Control Conference 2009, CDC/CCC 2009 (Shanghai, China 15-18 December, 2009) p. 1118-1123
- Publisher Link
- http://dx.doi.org/10.1109/CDC.2009.5399527
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- conference paper
- Date
- 2009
- Description
- This paper studies the stabilisation of switched discrete-time linear control systems under arbitrary switching. A sufficient condition for the uniform global exponential stability (UGES) of such systems is the existence of a common quadratic Lyapunov function (CQLF) for the component subsystems. The existence of such CQLF can be ensured using Lie-algebraic techniques by the existence of a nonsingular similarity transformation that simultaneously triangularises the closed-loop evolution maps of the component subsystems. The present work formulates a Lie-algebraic feedback design problem in terms of invariant subspaces and proposes an iterative algorithm that seeks a set of feedback maps that guarantee the existence of a CQLF, and thus UGES of the switched feedback system. The main contribution of the paper is to show that this algorithm will find the required feedback maps if and only if the Lie-algebraic problem has a solution.
- Subject
- Lie algebras; Lyapunov methods; switched systems; asymptotic stability; closed loop systems
- Identifier
- http://hdl.handle.net/1959.13/919096
- Identifier
- uon:8771
- Identifier
- ISBN:9781424438723
- Rights
- Copyright © 2009 IEEE. Reprinted from the Proceedings of the 48th IEEE Conference on Decision and Control 2009, held jointly with the 28th Chinese Control Conference 2009, CDC/CCC 2009. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
- Language
- eng
- Full Text
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