Realization theory for linear and bilinear hybrid systems

The paper deals with the realization theory of linear and bilinear hybrid systems, i.e. hybrid systems with continuous dynamics determined by linear ( respectively bilinear ) control systems. We will formulate necessary and sufficient conditions for the existence of a linear (bilinear ) hybrid system realizing the specified input/output maps. We will also present a characterization of a minimal linear (bilinear) hybrid realization and a procedure to convert a linear (bilinear) hybrid system to a minimal one. Partial realization of linear (bilinear) hybrid systems will be discussed too