Sufficient stability bounds for slowly varying direct-form recursive linear filters and their applications in adaptive IIR filters

This correspondence derives a sufficient time-varying bound on the maximum variation of the coefficients of an exponentially stable time-varying direc t-form homogeneous linear recursive filter. The stability bound is less con servative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output-error adaptive IIR filters to achieve bounded-input bounded-output (BIBO) stability of th e adaptive filter. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included. This corresponde nce also contains comparisons with other competing output-error adaptive II R filters. The results indicate that the stabilized method possesses better convergence behavior than other competing techniques.