The "generalized bilinear system" : a class of nonlinear discrete systems

A new class of nonlinear discrete-time systems is formulated and called the "Generalized Bilinear System (GBLS)". The well known bilinear system is a special class of this system, and hence the reason for the name. The GBLS is investigated for bounded input bounded output (BIBO) stability. It is shown that the GBLS is a special class of linear shift variant (LSV) systems. Three different sufficient conditions are established for the stability of LSV systems. Two of these conditions can be used in a very straightforward manner for monitoring the stability of a GBLS used as an adaptive filter.<>