On the stability of discrete time recursive Volterra filters

Many real nonlinear systems are characterized by an infinite input signal memory. In such conditions, system modeling by means of recursive polynomial filters requires a much lower number of coefficients with respect to nonrecursive realizations. However, the main problem of recursive polynomial filters is their inherent instability. This letter describes simple sufficient stability conditions for a class of discrete-time nonlinear systems based on recursive Volterra filters of arbitrary orders.