NDLI: Feedback stabilisation of switched systems via iterative approximate eigenvector assignment

Content Provider	IEEE Xplore Digital Library
Author	Haimovich, H. Braslavsky, J.H.
Copyright Year	2010
Description	Author affiliation: CONICET and Laboratorio de Sistemas Dinámicos y Procesamiento de Información, Departamento de Control, Facultad de Cs. Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Riobamba 245bis, 2000, Argentina (Haimovich, H.) \|\| ARC Centre of Excellence for Complex Dynamic Systems and Control, The University of Newcastle, Callaghan NSW 2308, Australia (Braslavsky, J.H.)
Abstract	This paper presents and implements an iterative feedback design algorithm for stabilisation of discrete-time switched systems under arbitrary switching regimes. The algorithm seeks state feedback gains so that the closed-loop switching system admits a common quadratic Lyapunov function (CQLF) and hence is uniformly globally exponentially stable. Although the feedback design problem considered can be solved directly via linear matrix inequalities (LMIs), direct application of LMIs for feedback design does not provide information on closed-loop system structure. In contrast, the feedback matrices computed by the proposed algorithm assign closed-loop structure approximating that required to satisfy Lie-algebraic conditions that guarantee existence of a CQLF. The main contribution of the paper is to provide, for single-input systems, a numerical implementation of the algorithm based on iterative approximate common eigenvector assignment, and to establish cases where such algorithm is guaranteed to succeed. We include pseudocode and a few numerical examples to illustrate advantages and limitations of the proposed technique.
Starting Page	1269
Ending Page	1274
File Size	175656
Page Count	6
File Format	PDF
ISBN	9781424477456
ISSN	07431546
e-ISBN	9781424477463
DOI	10.1109/CDC.2010.5717972
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-12-15
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation algorithms Algebra Algorithm design and analysis Bismuth Switches Optimization Linear matrix inequalities simultaneous triangularisation Switched systems arbitrary switching solvable Lie algebras common eigenvector linear matrix inequalities
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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