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.

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}, pages = {410--445}, publisher = {EDP-Sciences}, volume = {17}, number = {2}, year = {2011}, doi = {10.1051/cocv/2010014}, mrnumber = {2801326}, zbl = {1233.93020}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2010014/} }

TY - JOUR AU - Petreczky, Mihály TI - Realization theory for linear and bilinear switched systems: A formal power series approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 410 EP - 445 VL - 17 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2010014/ DO - 10.1051/cocv/2010014 LA - en ID - COCV_2011__17_2_410_0 ER -

%0 Journal Article %A Petreczky, Mihály %T Realization theory for linear and bilinear switched systems: A formal power series approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 410-445 %V 17 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2010014/ %R 10.1051/cocv/2010014 %G en %F 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://archive.numdam.org/articles/10.1051/cocv/2010014/

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