Filtered-X Lyapunov algorithm for nonlinear active noise control using second-order Volterra filter

This paper presents a filtered-X Lyapunov algorithm for nonlinear active noise control (ANC) using second-order Volterra filter-based the filter-blank structure. Unlike many adaptive filtering schemes using gradient algorithm, a Lyapunov function of the tracking error is first defined, and second-order Volterra filter coefficients are adjusted using Lyapunov stability theory so that the error converges to zero asymptotically. Moreover, it has fast error convergence property and its stability is guaranteed by Lyapunov stability theory.