Volume 17, Number 2, April-June 2011
|Page(s)||410 - 445|
|Published online||31 March 2010|
Realization theory for linear and bilinear switched systems: A formal power series approach
Part I: Realization theory of linear switched systems*
Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands. M.Petreczky@maastrichtuniversity.nl
Revised: 3 January 2008
Revised: 12 September 2009
The paper represents the first part of a series of papers 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 conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a characterization of 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 is admissible, but within this restricted set the switching times are arbitrary. The paper uses the theory of formal power series to derive the results on realization theory.
Mathematics Subject Classification: 93B15 / 93B20 / 93B25 / 93C99
Key words: Hybrid systems switched linear systems / switched bilinear systems / realization theory / formal power series / minimal realization
© EDP Sciences, SMAI, 2010
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