Stability analysis of robust adaptive filter used in feedforward and feedback compensation

This paper proposes robust adaptive algorithms for adjusting coefficients of an adaptive filter which is used for feedforward control together with a feedback compensator. The filtered-x algorithm which is widely employed in adaptive signal processing cannot always assure the stability. In this paper, stability-guaranteed adaptive algorithms are given in time domain and frequency domain on a basis of the strictly positive real property of adaptive systems in the presence of unknown disturbances. Time domain algorithms can be applied to an IIR or FIR adaptive filter, while frequency domain approaches use a structure of adaptive frequency sampling filter. Numerical simulations and experimentally obtained results exhibited significant improvement on convergency and stability of the proposed adaptive algorithms in application to adaptive active noise control.