On some connections between bilinear input/output maps and 2D systems

The aim of this contribution is to discuss some basic issues connected with bilinear i/o maps. We consider first stability problems, and derive necessary and sufficient conditions guaranteeing that baunded inputs always produce bounded outputs. These conditions refer to the singularities of a suitable rational function in two variables, and enlighten some connections between BIBo stability of 2D transfer functions and that of bilinear i/o maps. We analyse next the free system dynamics, namely the output evolution determined by finite support input sequences. Finally, assuming BIBO stability, we consider the asymptotic behaviour of the output associated with periodic inputs