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.

This paper is the second part of a series of papers dealing withrealization theory of switched systems.The current Part II addresses realization theory of bilinear switchedsystems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realizationtheory of linear switched systems.More precisely, in Part II we present necessary and sufficient conditionsfor a family of input-output maps to berealizable by a bilinear switched system, together with a characterizationof minimal realizations.Similarly to Part I, the paper deals with 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.