Discrete Sliding-Mode Adaptive Algorithm for adaptive filtering

This paper presents the discrete adaptive sliding-mode algorithm for adaptive filtering in signal processing. The parameter updated law of the adaptive filter is based on the FIR (Finite Impulse Response) model and is the non-switching type. The adaptive gain of the parameter updated law is adaptively adjusted to make the sliding variable to converge to zero in a finite duration. Then the gain is adjusted to keep the error dynamics in the sliding mode so that the desired error dynamics can be achieved in the sliding mode. The error dynamics are insensitive with respect to the bounded disturbances. The concept of the sliding mode was originally used for the design of robust control systems. Now it can be used for adaptive filter design to further improve the performance of adaptive filters. Simulation results are presented to illustrate the features of the proposed scheme. Key-Words: Adaptive filtering, sliding-mode, signal processing, Lyapunov stability theory