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Realization theory for linear and bilinear switched systems: A formal power series approach

Part I: Realization theory of linear switched systems*

Published online by Cambridge University Press:  31 March 2010

Mihály Petreczky
Mihály Petreczky*
Affiliation:
Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands. [email protected]
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Abstract

The paper represents the first part of a series ofpapers on realization theory of switched systems. Part I presents realization theory of linear switched systems,Part II presents realization theory of bilinear switched systems.More precisely, in Part I necessary and sufficient conditionsare formulated for a family of input-output maps to berealizable by a linear switched system and a characterizationof minimal realizations is presented. The paper treats two types of switched systems.The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences isadmissible, but within this restricted set the switching times are arbitrary.The paper uses the theory of formal power series to derivethe results on realization theory.

Keywords

Hybrid systems switched linear systemsswitched bilinear systemsrealization theoryformal power seriesminimal realization
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 2 , April 2011 , pp. 410 - 445
Copyright
© EDP Sciences, SMAI, 2010

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