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.

Classification: 93B15, 93B20, 93B25, 93C99

Keywords: hybrid systems switched linear systems, switched bilinear systems, realization theory, formal power series, minimal realization

@article{COCV_2011__17_2_410_0, author = {Petreczky, Mih\'aly}, title = {Realization theory for linear and bilinear switched systems: A formal power series approach}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {17}, number = {2}, year = {2011}, pages = {410-445}, doi = {10.1051/cocv/2010014}, zbl = {1233.93020}, mrnumber = {2801326}, language = {en}, url = {http://www.numdam.org/item/COCV_2011__17_2_410_0} }

Petreczky, Mihály. Realization theory for linear and bilinear switched systems: A formal power series approach. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 2, pp. 410-445. doi : 10.1051/cocv/2010014. http://www.numdam.org/item/COCV_2011__17_2_410_0/

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