Stability properties and periodic evolutions of bilinear systems in input-output form

Bilinear systems in input-output form are introduced and represented by means of suitable rational functions in two indeterminates. Necessary and sufficient conditions for bounded-input/bounded-output (BIBO) stability are derived and compared with analogous results on two-dimensional systems stability. Several features of the output evolutions corresponding to finite support as well as to periodic input sequences are discussed and related to the polar structure of the rational functions describing the input-output maps.